The tourists go down by five wickets after a blistering 89 from 49 balls by White is not enough to stop India taking lead in series.
Kohli century KOs Australians
Virat Kohli hit his highest one-day international score to lead India to a five-wicket win over Australia in the second one-day international at Visakhapatnam yesterday.
Kohli smashed 118, despite being hampered by a leg injury, to guide the hosts past Australia's 289 for three with seven balls to spare.
"I was struggling with cramps in my 70s and 80s, Kohli said. "I just wanted to drag the game as much as I could to put my team in a winning position.
"With Yuvraj [Singh] batting at the other end, it's always helpful because he can score quickly and take the pressure off you. We just decided to build a partnership and bank on the powerplay.
"The team has shown trust in me to bat at No 3 and I'll just look to capitalise. Once the dew came in, the ball was coming on quite nicely and we tried to take advantage on that."
Michael Clarke, the stand-in Australia captain, had earlier returned to form as he hit his fifth ODI century, although his knock of 111 was overshadowed by a blazing late innings from Cameron White.
White smashed an unbeaten 89 from just 49 balls as the tourists took 114 from the final 10 overs to set a testing chase.
"Cameron's innings was unbelievable," Clarke said. "I thought 290 was enough but India chased well … disappointed with the result. We'll try to do better in the first 15 overs in the second game."
Even White's innings was not enough as the 21-year-old Kohli displayed maturity beyond his years, with the aid of half-centuries from Suresh Raina and Yuvraj, to guide India to a 1-0 lead in the three-match series, which saw the opening game ruined by rain.
With both teams opting to rest most of their star names, there were two new faces in each team.
Left-handers Shikhar Dhawan and Saurabh Tiwary made their India debuts while Australia fielded an inexperienced bowling attack after bringing in the untried duo of Mitchell Starc and John Hastings.
That meant Nathan Hauritz, who has come in for criticism for his performances so far on tour, was easily the tourists' most experienced recognised bowler with 55 ODI caps.
It was the hosts' inexperience, however, that was exposed early in India's chase as Dhawan was bowled by Clint McKay from the second ball of the innings without scoring.
McKay then induced an edge from Murali Vijay to leave India in trouble at 35 for two, before Kohli set about his task.
The right-hander was struck down by a leg injury, which left him needing a runner, but he anchored the innings, first in a stand of 137 with Yuvraj.
Yuvraj had added 58 before he became McKay's third victim, bowled by a slower ball, but Kohli was unmoved as he and his new partner Raina picked off Australia's young attack.
The pair combined in an 84-run stand in quick time to ensure the hosts could afford a minor slip when Kohli's memorable knock did end with them 34 runs short of the target. Raina reigned in his earlier aggression to make sure he guided his side home with an unbeaten 71 from 47 balls.
MS Dhoni, the India captain, said: "We'll look to win the third game as well. We have eight to 10 games before the World Cup and we want to achieve more than just winning the games."
Marsh b Nehra 0
Paine c V Kumar b Nehra 9
Clarke not out 111
Hussey lbw b Ashwan 69
White not out 89
Extras 1w, 10lb 11
Total (3 wkts, 50 overs) 289
Fall of wickets: 1-11; 2-16; 3-160
Bowling: P K umar 9-1-51-0; Nehra 10-1-57-2; V Kumar 9-1-71-0; Ashwin 9-0-34-1; Vuvraj 10-0-48-0; Raina 3-0-18-0;
Dhawan b McKay 0
Vijay c Paine b McKay 15
Kohli c Hopes b Hastings 118
Vuvraj b McKay 58
Raina not out 71
Dhoni b Hastings 0
Tiwari not out 12
Extras 9w, 8b, 1lb 18
Total (5 wkts, 48.5 overs) 292
Fall of wickets: 1-0; 2-35; 3-172; 4-256; 5-257
Bowling: McKay 10-0-55-3; Starc 8.5-0-51-0; Hastings 10-1-44-2; Hopes 7-0-56-0; Hauritz 10-0-54-0; Smith 3-0-23-0
India won by five wickets.