Sydney: Virat Kohli marked his elevation to India's captaincy by smashing his fourth century of the series on Thursday, leading the visitors to 342-5 after day three of the fourth test, trailing Australia's total by 230 runs.
Lokesh Rahul also scored his maiden century and Rohit Sharma made 53 as India moved to the brink of avoiding the follow-on.
Kohli, who was appointed captain when Mahendra Singh Dhoni suddenly retired after the third test, produced an unbeaten 140 to go with his twin centuries in the first test and his highest score of 169 in the third test.
Kohli's four tons in the series matches the effort of Australia's stand-in skipper Steve Smith, who is the heir apparent to the injured Michael Clarke as permanent captain, and as young leaders they may be establishing a longstanding rivalry.
"It's been a hundred feast this test series and to see them both play and the way they've captained their sides has been exciting times ahead for both countries," Australia coach Darren Lehmann said.
The 26-year-old Kohli has 639 runs for the series and passed Rahul Dravid's record of 617 runs in a series (2003-04) by an Indian batsman in Australia.
Rahul — playing his second test after a poor debut in Melbourne with scores of 3 and 1 — reached his milestone with the aid of an incorrect bat-pad decision, a missed run out chance and a dropped catch which was partly caused by interference with a TV camera suspended above the field.
"I'd say I'm more relieved than proud of myself," said Rahul. "It was a nightmare debut and it didn't make my life easier coming here. I just kept telling myself the only way from here is up."
Mitchell Starc (2-77) toiled on a placid SCG pitch to finally remove Rahul for 110 caught and bowled.
Shane Watson (2-42) trapped Ajinkya Rahane lbw for 13, before having Suresh Raina (0) caught behind next ball to reduce India to 292-5 and revive hopes of enforcing a follow-on.
Wriddhiman Saha was 14 not out with Kohli at stumps, having added 50 for the sixth wicket.
Australia did have opportunities to take more wickets, but missed a simple run out chance and dropped two catches during day three.
Rahul, when on 46, skied a Shane Watson delivery high in the air behind the stumps. Smith ran back from slip to take the catch but reacted angrily after putting down the chance, pointing toward the wires of the aerial camera.
Cricket Australia and the host broadcaster, the Nine Network, later released a joint statement confirming Smith had been "distracted by one of the wires in his eyeline."
"It wasn't ideal where it was positioned for that particular ball," said Lehmann. "I like watching it, but they have to get the position right when the bowlers are bowling."
Kohli's only mistake came on 59 when he edged a Starc delivery with the second new ball to Smith at third slip, where the captain dropped the sharp chance above his head.
"A couple of tough chances, but you still have to take those on wickets that will deteriorate on days four and five," said Lehmann. "We needed to speed up the game today, so a little bit disappointing. But there's still a lot of time in this game."
In the first session, Lyon appealed for a bat-pad catch off Rahul but it was turned down by the umpire. Infrared video replays showed the ball had lightly flicked Rahul's glove before hitting his thigh and popping up for Joe Burns to catch.
Lyon did bowl Sharma for 53 next over, catching the bottom edge as Sharma attempted to sweep.
Australia should have removed Rahul on the next ball. At the non-striker's end, he began running for a single when the ball deflected off wicketkeeper's Brad Haddin's leg to short fine leg, but turned back, slipped over and scrambled back to his crease before fielder Starc or Haddin were aware of the simple run-out opportunity at the bowler's end.
The hosts have an unassailable 2-0 series lead, and regained the Border-Gavaskar trophy, with two wins and a draw in the first three tests.