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Henriques followed up his first innings half century with another gutsy effort as he added 57 runs for the final wicket with No 11 Nathan Lyon (8 batting) to prevent India from wrapping up the match with a day to spare.
The duo consumed 18.1 overs to not only frustrate the hosts but also snatch a lead of 40 runs as they ended the day at 232 for nine. This was after Ravichandran Ashwin's second five wicket haul helped India decimate the Aussie top and middle-order.
Ashwin grabbed five for 90 and his current match haul of 12 wickets helped India reduce Australia to 175 for nine before Henriques-Lyon provided some rearguard action to ensure that the game went into the final day.
With pitch providing right kind of assistance for the spinners, senior-off spinner Harbhajan Singh also put up a much improved performance in the second innings scalping the important wickets of David Warner and Matthew Wade.
The duo were ably complemented by all-rounder Ravindra Jadeja, who also helped the team with important breakthroughs.
The highlight of India's performance was skipper Mahendra Singh Dhoni's magnificent 224 which enabled the home team to post a mammoth 572 in their first innings, thereby ensuring a lead of 192 runs.
The likes of Ed Cowan (32), Michael Clarke (31) and David Warner (23) tried their best but it was a near-impossible task to play a game of survival on a pitch that was deteriorating with the passage of every over.
Batting more than five sessions to save the Test match was a Herculean task but Shane Watson and Cowan showed intent during the first session.
Ashwin struck with the last ball before lunch. He invited Watson to play forwarded but ball took off the surface to hit the shoulder of his bat as Sehwag took the catch. However the post lunch session spelt doom for the visitors as they lost four top-order batsmen during the session.
Resuming at overnight 515 for eight, India added another 57 runs to the total with skipper Mahendra Singh's epic double hundred finally ending at 224.
In reply, Australia showed some early determination but opener Shane Watson (17 of 46 balls) fell to the last delivery before lunch to give India the upperhand.
Ed Cowan (13) was holding fort at the other end with David Warner to join him after the break on a turning track, where India opened the bowling with spinners at both ends.
Watson's wicket went in off-spinner R Ashwin's kitty. The ball turned and kissed the all-rounder's glove before being safely taken by Virender Sehwag in the slips, giving Ashwin his first of the innings and eighth overall wicket in the match.
Earlier in the morning, Dhoni and tailender Bhuvneshwar Kumar (38) continued from where they had left yesterday and frustrated the Australian bowlers with deft strokeplay and quick movement between the wickets.
Dhoni, however, could not cross the individual milestone of most runs in an innings by a keeper-batsman, which will continue to remain with Zimbabwean Andy Flower (232).
Nonetheless, it was a career-best effort from Dhoni, who finally departed in the 147th over of the Indian innings. The gutsy skipper fell to young pacer James Pattinson, becoming his fifth wicket of the match.
Dhoni, who put on 140 runs for the ninth wicket with Bhuvneshwar, was dismissed after striking 24 fours and half a dozen sixes, including one this morning, during his 265-ball knock.
The odd duo scored at a rate of over four runs during their partnership which lasted 31.1 overs. Dhoni's contribution in the stand was a whopping 103.
His domination of the Australians ended when he edged a bouncer from Pattinson to his wicketkeeping counterpart Matthew wade.
The 31-year-old walked off the ground to a standing ovation from the crowd and the dressing room.
His dismissal, however, didn't immediately bring the curtains down on the Indian innings as Bhuvneshwar and Ishant Sharma (4 not out) combined for a last-wicket stand of 26 to leave the Aussies flustered.
The visiting side's agony ended in the 155th over when pacer Peter Siddle finally got rewarded for bending his back hard for the past two days.
The pacer tasted success in his 25th over when Bhuvneshwar gave an easy catch to Michael Clarke at mid-off.
The debutant also walked back to a standing ovation from his teammates after a lion-hearted 38-run effort that helped his skipper build the innings.
Bhuvneshwar's 97-ball knock was studded with four hits to the fence.