The hosts' spinners proved to be vital on the deteriorating pitch on the fourth day of the opening Test after they were declared all out on 572 in the morning session following a mammoth innings from MS Dhoni (224).
The Aussies were dealt a blow before lunch when they lost Shane Watson for 17 courtesy of a bowl from Ravichandran Ashwin, and wickets continued to tumble in the second session when Ed Cowan (32) and Phillip Hughes (0) were dismissed in quick succession.
Michael Clarke, who had plenty of pressure on his shoulders to rack up the runs for the visitors when he came to the crease, had an assured start but it was Ashwin who came out on top by sending the batsman out with an lbw on 31 runs.
The responsibility fell to Henriques, who managed to stay composed as wickets fell around him, and ensured that India will have to bat tomorrow after surpassing Australia's target courtesy of an unbeaten 75.
The visitors currently lead by 40 runs with one wicket remaining.