Virat Kohli became the first man ever to make three Test centuries in his first three innings as captain and Lokesh Rahul made the first of his career as India fought back on day three of the fourth Test against Australia at Sydney.

The hosts had declared on 572 on day two but India produced a brilliant response to reach 342 for five, a deficit of 230, with Kohli hitting his fourth ton of the series as the pair put on 141 for the third wicket.

Rahul had reached 110 when he was dismissed in just his second match while Kohli, in his first match as full-time skipper following the shock resignation of Mahendra Singh Dhoni, was undefeated on 140.

India began the day on 71 for one and made slow progress in the early stages, adding just 12 runs in the first 10 overs.

Despite the slow going, Rohit Sharma brought up his half-century off 132 balls but was gone to the next one he faced as he edged a Nathan Lyon delivery onto the stumps to depart for 53.

A major talking point then came three overs before lunch when Rahul did not get hold of a pull off Shane Watson and the ball went flying into the air with Steve Smith looking certain to make the catch.

The stand-in captain, though, spilled the opportunity and instantly pointed to the sky, suggesting the ball may have hit the ‘spider-cam’ system of camera wires above the pitch.

Both Cricket Australia and the Australian broadcasters later confirmed that was not the case but admitted Smith had been “distracted by one of the wires in his eye line” and the fielder looked furious to have spilled the opener on 46.

The rate did not pick up a great deal after the interval but the batsmen were clearly comfortable in the middle, finding the boundary with anything loose, and Rahul moved into the 90s with a six off Lyon.

Kohli then reached his half-century before the new ball was taken and Mitchell Starc almost had the skipper through the gate first ball but it took a slight inside edge and went to the rope.

Smith then put down another chance but this time he had nobody to blame but himself as Kohli got on an edge to a Starc ball and it flew high to second slip where Smith spilled the opportunity above his head.

More drama was to come before tea as Rahul, who had recorded scores of three and one on debut in Melbourne, brought up his maiden Test ton off 253 balls as he guided the ball to the rope past gully.

His joy was short lived, however, as in just the second over after tea he was gone, pulling a Starc delivery high into the air and the bowler claimed the catch himself at the batsman’s end.

That seemed to prompt Kohli to want to race to his century and the right-hander joined counterpart Smith in making it four for the series off 162 balls.

It had very much been the tourists’ day so far but Watson changed the complexion slightly with two wickets in as many balls in the 100th over.

First Ajinkya Rahane was trapped in front for 13 and then Suresh Raina edged to Brad Haddin, who made an impressive catch diving to his left.

That could have had India wobbling but Kohli and Wriddhiman Saha (14 not out) made it through to the close with the former becoming the top Indian run-scorer in a series in Australia.