The 32-year-old, playing her 18th year on tour, drew on all her experience to ease past the Frenchwoman 6-3, 6-3 on centre court in 77 minutes.
Williams has been battling injury and illness in the past two years and her ranking has dropped, but she has clawed her way back to be 26.
She knows she will have to dig deep against Sharapova.
"I look at the draw, I'm not superstitious," she said after the match. "I play Maria and I better bring my best game against her."
Meanwhile Sharapova handing out a tennis lesson to young Japanese player Misaki Doi in a one-sided rout.
The Russian world number two, champion in 2008 and runner-up last year, hardly raised a sweat in trouncing the 21-year-old 6-0, 6-0 in just 47 minutes on Hisense Arena.
Second seeded Sharapova is in imposing form and has now won 24 games in a row after also scoring a rare 6-0, 6-0 double bagel against hapless first round opponent Olga Puchkova.
Doi, ranked 97, was always going to struggle and appeared to be overawed by the occasion, having no answers to Sharapova's power and precision shot-making.
There was little the Japanese, in her first Australian Open, could do but learn a lesson as the Russian bagged the first set in just 23 minutes, and it was more of the same in the 24-minute second.
Sharapova now faces the tantalising prospect of a third round clash with seven-time Grand Slam winner Venus Williams, who plays in an evening match.
Fourth seed Agnieszka Radwanska stormed to her 11th straight win of the year to build on her sizzling start to the season.
Radwanska continued her early form with a routine 6-3 6-3 defeat of Romania's Irina-Camelia Begu on Rod Laver Arena.
The Pole has now won 11 straight matches in 2013 without dropping a set - a run which saw her claim the titles in Auckland and Sydney heading into the season's first grand slam event.
She will play the winner of the match between British number one Heather Watson and Ksenia Pervak next.
Australian world number nine Samantha Stosur threw away the last five games to hand China's Zheng Jie passage to the third round in a nervy and hard-fought clash.
Stosur, who suffered first-round flops at WTA events in Brisbane and Sydney this year, was leading 5-2 in the third set but choked in front of her home fans and double faulted to hand Zheng victory 6-4, 1-6, 7-5.
Zheng, coached by husband Zhang Yu, she executed her favourite backhand shot with precision to rattle the Australian who has long struggled in front of her home crowd.
The set went with serve until Zheng got the crucial break in the seventh game. Stosur immediately broke back but got broken once again to put the Chinese 5-4 in front and set up a nerve-tingling final game.Stosur saved seven set points, including one rally of 28 shots, in a game that lasted more than 12 minutes before she sent an easy overhead volley long to hand Zheng the set in 54 minutes.
But cheered on by a boisterous crowd on Rod Laver Arena, Stosur came out for the second set fired up and broke Zheng in the fourth game en route to levelling the match.
Now in her rhythm, Stosur got an early break in the third but Zheng refused to wilt and under pressure, it was the Australian who caved in meekly to miss out on a third round clash with 18th seeded German Julia Goerges.
Fifth seed Angelique Kerber was also hardly troubled as she breezed past Lucie Hradecka 6-3 6-1.
The German, however, claimed the match was harder than the score line suggested, saying: "She's a tough opponent and you need to be ready for the whole match because she's playing the ball very hard and deep in the court.
"I was just trying to move well and play my game.
"I'm happy that I won in two sets."
Li Na, a finalist here two years ago, had to hit back from 5-3 down in the second set to complete a 6-2 7-5 success against Olga Govortsova.
Julia Goerges, the 18th seed, also advanced early on day three but there were two surprises.
Dominika Cibulkova, the 15th-seeded Slovakian, was stunned 7-6 (8/6) 6-4 by Russian qualifier Valeria Savinykh while number 23 Klara Zakopalova won just one game against Belgium's Kirsten Flipkens.
Novak Djokovic turned in a dazzling demolition of Ryan Harrison as he stormed into the third round.
The world number one was in irresistible form, outclassing the young American 6-1, 6-2, 6-3 in just 1hr 31min of high-class tennis on Rod Laver Arena.
Djokovic, a three-time winner and going for three straight Australian titles, will next play Czech journeyman Radek Stepanek in the last 32.
"I tried to focus on the start and I knew that he had nothing to lose and would come out with his big serves, but I managed to make some very important early breaks at the start of the match," Djokovic said.
"I was a set up after 20 minutes and it was a mental advantage, I felt much more comfortable on the court.
"I don't think he was playing at his best, it was probably the occasion playing on the centre court, but I wish him all the best, I think he has a good future."
Spanish fourth seed David Ferrer needed five match points before subduing American Tim Smyczek in four sets to reach the third round.
Ferrer was extended by the 125th-ranked American before clinching a 6-0, 7-5, 4-6, 6-3 win in 2hr 38min on Margaret Court Arena to take his place in the last 32 of the tournament.
The Spaniard looked to be heading for a regulation straight-sets victory but the tenacious Smyczek broke him twice to take the set and keep Ferrer longer out on the court.
Smyczek, despite being treated several times at changeovers by the trainer for a tight right thigh, chased down everything and Ferrer needed five match points before finally prevailing.
"I'm OK because I've won the match and he gave a good performance. I don't have any physical problems, so all's good," Ferrer said afterwards.
"I will rest this afternoon and tomorrow and get ready for my next match."
Fifth seed Tomas Berdych swept into the third round with a straight sets win over Frenchman Guillaume Rufin.
Berdych was too strong for the 92nd-ranked Rufin, winning 6-2, 6-2, 6-4 in exactly 2hrs.
He was in little bother breaking Rufin's service six times and hitting 30 winners to 19.
"I don't know how many matches he has played on the big arena, but from what I know from my experience that it's quite tough to play one of the first matches like that," Berdych said afterwards.
"I had to work hard to win in three sets. It was a better match for me from the first round and that's what I always like to do improving one by one and not just bringing my best tennis for the first round.
"It was a quite solid game from me and I hope I can improve on that for the next round."
Jerzy Janowicz exploded in rage after losing a 79-minute set to India's Somdev Devvarman, hitting the umpire's chair with his racket and throwing his water bottle across court.
The Polish 24th seed furiously contested a line call in the opening set of their second round tie on court eight, collapsing to his knees in frustration with his forehead touching the playing surface.
His Indian opponent took the tiebreaker 12-10 to win the set and at the changeover, Janowicz again argued his case with Croatian umpire Marija Cicak before making the point more forcefully with his racket.
While he was regaining his composure, Devvarman raced away with the second set 6-3 but the Pole hit back with 15 winners to win the third 6-1 and the fourth 6-0 to level up the match.
Devvarman, who reached a career-high 62nd in the world in July 2011, has slipped to 551 after missing most of the 2012 season with a shoulder injury.
As India's sole remaining representative in the single's draw at Melbourne Park, Devvarman's participation in the match would have guaranteed a huge TV audience for Janowicz's tantrum.
Janowicz faces sanctioning from the International Tennis Federation for angrily hitting the umpire's chair with his racquet at the completion of the first set.
"The umpires, they're making so many mistakes," Janowicz said."One of the most important mistakes was set point in the tiebreak, 9-8. Was a shanked forehand from Devvarman. The ball was really slow, it was clean out," he said.
"I was already happy, I was already shouting 'come on.' But the referees didn't say anything. This was the moment when I went nuts.
"Sometimes it happens like this. Sometimes I have a problem to control my emotions, but I'm trying to work on this."
The ITF will announce on Thursday if Janowicz will be fined.
Devvarman said he had never witnessed an outburst like the one delivered by Janowicz, whose tantrum was attracting a stream of YouTube viewers shortly after the match.
"I was thinking dude, relax," Devvarman said."He is a friend and I have played him before. He got a little upset with a couple of calls."
Japan's Kei Nishikori wore down Argentina's Carlos Berlocq to reach the third round.
The 16th seed surged home after being taken to a first set tiebreaker to oust the 68th-ranked Berlocq, 7-6 (7/4), 6-4, 6-1 in 2hr 18 min.
Nishikori, flying the flag for the Asian men at the year-opening Grand Slam, dominated with his forehand and court speed as he reeled off 47 winners and six service breaks to take his place in the last 32.
The Japanese star, who reached the quarter-finals of last year's Australian Open in the best ever Grand Slam performance by a Japanese man, had a battle in a 69-minute opening set.
But once he got the initial edge he proceeded to take charge, and grabbed three service breaks in the second set and another two in the final set to win easily.
Nishikori showed no problems with a left knee injury that forced him out this month's Brisbane International and Kooyong Classic tournaments.
He will play either 23rd seed Mikhail Youzhny or another Russian, Evgeny Donskoy, in the next round.
American Brian Baker's hopes of a fairy tale run at the Australian Open were dashed in the cruellest of fashions when he was forced to retire from his second round match with a knee injury.
The 27-year-old, who returned last year after seven years off the professional circuit, had won the first set against compatriot Sam Querrey in a tiebreaker and was level at 1-1 in the second with the 20th seed when he suffered the injury.
"I didn't see what happened," Querrey said afterwards. "I hit a ball, and then he hit a ball long. I was looking at the ball kids to grab balls for my serve, and then I looked back and he was on the ground.
"And then just asking him, he said he kind of just felt his knee almost buckle and kind of heard like a pop or a snap. He didn't know if it was bones or a tear, but he couldn't straighten it, couldn't walk.
"I feel awful for him."
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