Clarke brought up his 23rd Test century off the second last ball of the day hitting left-arm spinner Ravindra Jadeja towards long-off to remain unbeaten on 103 on a day whih saw an engrossing battle between the bat and the ball.
Clarke negated all the good work done by off-spinner Ravichandran Ashwin (6/88) who took all but one among seven wickets that fell on the day at the Chepauk.
Clarke was well-complemented by debutant Moises Henriques (68) as the pair added 147 runs for the sixth wicket after Ashwin's terrific post-lunch spell saw the visitors being reduced to 153 for five.
The Tamil Nadu offie finally broke the partnership by dismissing the impressive Henriques, trapping him leg-before much to the relief of his teammates.
Ashwin, who took his sixth five-wicket haul in Test matches ended with fantastic figures of six for 88 in 30 overs but should consider himself unlucky being robbed off Clarke's wicket due to the absence of Decision Review System (DRS).
The Australian captain was batting on 39 when he offered a simple bat-pad catch to Cheteshwar Pujara at forward short-leg but umpire Kumar Dharmasena turned down the vociferous appeal from the Indians.
The television replays clearly indicated that the ball had hit Clarke's bat before flying off to the close-in fielder. The rival skipper took advantage of the situation and did not look back as he took his team to a position of safety with other Indian bowlers looking pedestrian.