India were going strong with Rahul and Kohli having settled well and looking to further their partnership and ease India into the match in the final session.
But the former was out quickly, top-edging Starc as the bowler gleefully accepted the return catch.
Rahul got a reprieve when on 46 as he top-edged Shane Watson (0/10) in the 53rd over, only for Steve Smith to run back from first slip but drop the skier as he was distracted by the cables of the overhead spidercam hung atop the SCG.
After Rahul's dismissal, Ajinkya Rahane (13) came to the crease and quickly added 50 runs for the fourth wicket with Kohli, thanks mainly to the Indian captain who just pushed on.
In the 97th over of the innings then, Kohli brought up his 10th Test hundred off 162 balls. In doing so, he became the first Indian batsman after Sunil Gavaskar (in 1971 and 1978-79 versus West Indies) to score four centuries in a Test series.
Kohli also became the first overseas batsman since Herbert Sutcliffe (1924-25) and Walter Hammond (1928-29) to score four hundreds in a Test series in Australia. He also went past Dravid's tally of 619 runs accumulated in the four-Test series against Australia on the 2003-04 tour.
Afterwards, there was a mini-collapse as Watson struck twice in the 100th over to remove Rahane lBW and then had Raina caught behind off successive balls. Saha managed to see off the hat-trick ball and then stayed on with his skipper till the end of play as India are still 31 runs adrift of the follow-on mark.
Earlier, in the post-lunch session, Rahul and Kohli looked to bat for long with the ball not doing much and the pitch still an easy one to bat on. And they were quite successful in doing as the runs started flowing after the dry morning session.
India had only scored 51 runs in two hours' play before lunch, but they made amends as 45 runs came in the first hour and then another 67 runs in the next hour until tea as normalcy was restored.
Much of this could be attributed to Kohli's batting as he raced to his fifty off 108 balls. He was though lucky to be still at the crease with Steven Smith (0/12) dropping a second catch in the day, this time at second slip off Mitchell Starc (1/50) in the 83rd over, just after the second new ball had been taken. Kohli was batting on 59 then.
Young opener Rahul also overcame his horrific debut Test in Melbourne to achieve a milestone. Rahul got to his century in the 85th over, the last before tea, off 253 balls.
In the morning session, India had fought hard with runs trickling in. Rohit Sharma (53 off 133 balls) and Rahul started off for India from their overnight score of 71/1. They needed to bat for time as well as keep the runs ticking.
While they were successful at the first part, runs came in a trickle as the Australian bowling attack bowled with patience on an easy pitch. They held a tight line and length and gave very little for the Indian batsmen to play against.
Only 19 runs came off the first hour of play which saw 15 overs bowled. Only three boundaries came in that run of play, two off the bat of Rahul and one from Rohit. However, if the first hour was a little dull, there were many interesting things waiting to happen in the second part of this morning session.
It started with Nathan lyon's (1/39) introduction into the attack as he got the ball to bounce and turn, using the rough marks to his advantage. In the 44th over, he had a close shout for a catch against Rahul (on 42 then) turned down, despite the replays showing that the batsman might have had a feather-nick to Joe Burns at short leg. It did not matter much as he got Rohit on the fourth delivery of that over.
It was the first ball Rohit faced off the spinner and he went for an expansive sweep, only to get a bottom-edge onto his stumps. The batsman walked off dejected, having only reached his second Test fifty, off 132 balls in the previous over bowled by Ryan Harris (0/30).
It brought Kohli to the crease and was immediately beaten by lyon off the first ball. The batsman nearly set off for a run and the non-striker, Rahul (still on 42) came half-way down the crease only to be sent back. It was a great run-out chance for Australia but substitute fielder Pat Cummins threw to the wrong end.