Rivals Federer and Nadal could meet in the quarter-finals of the BNP Paribas Open.
Roger Federer eases through, Rafael Nadal gets a bye and Victoria Azarenka struggles at Indian Wells
Spaniard Nadal, twice champion at Indian Wells, was gifted his spot when Argentina's Leonardo Mayer withdrew with a back injury before the start of their third-round match.
Federer, a four-times winner of the ATP Masters 1000 event, had minor back problems of his own but progressed with a commanding 6-3, 6-1 victory over Croatia's Ivan Dodig in a contest lasting just 61 minutes.
Federer and Nadal last met a year ago, also at Indian Wells, when the Swiss won a semi-final battle 6-3, 6-4.
Federer tweaked his back during the latter stages of his match against Dodig, but with a rest day on Tuesday he was not worried that it could affect his last 16 match on Wednesday.
"It's not the first time it's happened in my career, so, I know how to deal with it," said the world No 2.
Federer will next meet compatriot Stanislas Wawrinka or Australian Lleyton Hewitt, who play later on Monday at the Indian Wells Tennis Garden.
"I'm walking fine, I have a day off tomorrow. Everything is all right," added Federer. "It's happened during grand slams, during tournaments, in practice.
"It's just something you learn to deal with. And as long as I keep on playing, it's all right. I also know I have a longer break to recover so, from that standpoint, I'm not worried at all."
World No 5 Nadal, who is competing in his first tournament on a hardcourt surface in almost a year, was saddened when he learned that Mayer had withdrawn.
"That's bad news, for sure, for the fans and for Mayer, especially," said the Spaniard, who will next face Latvian Ernests Gulbis. "I talked with him. It seemed like it's nothing very, very bad.
"Just a typical back problem, beginning when he was warming up his serve. The physio says maybe in four days, five days he will be ready.
"That's the most important thing, that nothing is serious," said the Spaniard, who was sidelined for seven months last year by a left knee injury.
Though Nadal has beaten Gulbis in their four previous meetings, the Latvian looked forward to challenging the Spaniard after winning his 13th consecutive match on Monday.
"When was the last time I won 13 matches in a row?" 67th-ranked Gulbis said after fighting back to beat Italy's Andreas Seppi 5-7, 6-3, 6-4. "Of course he's a great player, but I honestly believe that if I play my best game I can beat him.
"I like to play against him because his ball and his heavy spin, it's good for my timing. I don't like it when the opponents hit flat, deep balls."
Second-seeded Federer, the defending champion at Indian Wells, improved his win-loss record this year to 12-3 after overcoming Dodig in their first meeting.
Dodig gave the Swiss a tough challenge early on and the opening set went with serve until the eighth game when the Croatian made two consecutive double faults to be broken.
Federer then needed four set points to serve out, finally clinching the set in 34 minutes with a service winner that left his opponent floundering.
The Swiss maestro then took firm control, breaking Dodig in the first game, when the Croatian netted a backhand, and also in the third, when his opponent again double faulted.
Federer sealed victory by breaking Dodig for a third time, the match ending on yet another double by the 60th-ranked Croatian.
In other matches, sixth-seeded Czech Tomas Berdych eased past Germany's Florian Mayer 6-4 6-1 while 10th-seeded Frenchman Richard Gasquet swept aside Poland's Jerzy Janowicz 6-1, 6-4.
Meanwhile in the women's category, Victoria Azarenka woke up just in time, rallying for a 3-6, 6-3, 6-0 victory over Belgian Kirsten Flipkens that kept her title defence on track.
Azarenka remained unbeaten in 2013, having successfully defended her Australian Open title and her WTA Doha crown.
The 23-year-old from Belarus, currently ranked second in the world behind American Serena Williams, is vying to become the first woman to win back-to-back titles at Indian Wells since Martina Navratilova in 1990 and 1991. But she showed far from dominant form in a scrappy first set against Flipkens, a 27-year-old ranked 31 in the world.
"I just wanted to go to sleep instead of playing tennis," Azarenka said of her first-set struggles, which saw her broken three times in the frame after taking a 2-0 lead.
A stuffy nose compounded her problems, and once she had dealt with that, she said, she began to feel better. "I just blew my nose, started breathing better and calmed down and started to see what I had to do," she said.
Nevertheless, after she had held her serve to open the second set she and Flipkens exchanged breaks in the next four games before Azarenka earned the decisive break in the eighth. She served it out with a love game and a demoralised Flipkens had no answer in the third.
Even though it was not her best, Azarenka said it was a gratifying victory, one that showed she's maturing as a player. "I'm really happy that I find the ability to turn around my matches no matter what the circumstances are on the court," she said.
"That's definitely what excites me the most. To know when to take your opportunities, when to do things is definitely a learning experience. I'm glad I'm starting to master that."
Azarenka, who next faces unseeded Urszula Radwanska of Poland, led a parade of the top 10 seeds into the women's round of 16 scheduled for Tuesday.
Second-seeded Maria Sharapova, No 3 Agnieszka Radwanska and fifth-seeded Petra Kvitova had advanced on Sunday.
The No 4 seed Angelique Kerber of German advanced with a 6-1, 7-6 victory over Belgian Yanina Wickmayer. Seventh-seeded Australian Sam Stosur, a former US Open champion, defeated China's Peng Shuai 6-3, 3-6, 6-2 and eighth-seeded Caroline Wozniacki breezed past Russian Elena Vesnina 6-2, 6-1.
Kerber had to dig deep in the second set but said words of encouragement from her coach when she trailed 4-1 helped her turn it around.
"He was coming to me and just reminding me of the game plan we had before the match and just telling me to focus on my game, play point by point and believe in my game," she said. "It helps me."
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