Captain Virat Kohli smashed his fourth century of the series while young Lokesh Rahul also hit a gritty maiden ton as India fought to keep themselves afloat on day 3 of the fourth and final cricket Test against Australia at the Sydney Cricket Ground on Thursday.
Kohli, produced a sparkling 140 with 20 boundaries to go with his twin centuries in the first test at Adelaide and his highest score of 169 in Melbourne's third test.
The 26-year-old 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, earlier reached his milestone, having survived an incorrect bat-pad decision, a missed run out and a dropped catch which was partly caused by interference with a TV camera suspended above the field.
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.
But Kohli and Wriddhiman Saha (14 not out) added 50 runs for the sixth wicket to take India to 342/5 at stumps.
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."
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.
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 was not left disappointed for long as he bowled Sharma for 53 next over, catching the bottom edge of Sharma's bat as he attempted to sweep the off-spinner to the leg side.
Australia should have removed Rahul on the next ball as Lyon beat new batsman Kohli and the ball deflected off wicketkeeper Brad Haddin's leg to Starc at short fine leg.
Rahul set off for a quick single, before turning back, slipping over and scrambling back to safety at the bowlers end before Starc and Haddin were aware of the simple opportunity to run the batsman out, much to captain Smith's frustration on a trying day for the hosts.
Australia declared its first innings at 572-7 just after tea Wednesday, with its top six batsmen all scoring above 50 for the first time, including centuries for Smith (117) and David Warner (101).
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.