Resuming at 316 for 7, the visitors resisted home attack for 38 overs and added 64 runs although a few decision went in their favour which further added to India's frustration.
Since the last-wicket pair of James Pattinson and Nathan Lyon was at the crease at the official lunch time, the morning session was extended and at the fall of the latter, the break was taken.
Indian off-spinner R Ashwin registered his career-best figures (7/103) while Ravindra Jadeja (2/71) took two wickets.
Clarke stepped out to loft Jadeja over his head for a straight six but just managed an edge that flew to the hands of Bhuvaneshwar Kumar at long-off.
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Clarke's splendid 130-run captain's knock came off 246 balls with 13 boundaries including one shot over the fence. It also ended 54-run fighting stand between him Siddle (19).
Soon, Harbhajan Singh's long wait to get a wicket ended when he had Siddle caught at first slip. Playing his 100th Test and going wicket-less on the opening day, it took the off-spinner the last ball of his 24th over to get his first.
However, Siddle did a fantastic job for his side, facing 94 balls during his stay, supporting his skipper well.
Harbhajan was extremely unlucky to not get next-man-in Pattinson out leg before in his next over as umpire Kumar Dharamsena turned down the confident appeal.
It was a faster delivery, hitting the back pad of Pattinson in front of the stumps but Dharamsena was unmoved, leading to an argument between a livid Harbhajan and the umpire.