According to the supersport.com website, Australia were in trouble at tea on 128 for five needing another 64 runs to force the hosts to bat again. After the break India kept pegging away at the Baggy Greens' resistance and the visitors lost their ninth wicket still 17 runs adrift.
However, Henriques buckled down and together with Nathan Lyon (eight) the pair miraculously not only survived until stumps, but managed to put together an unbeaten 57-run partnership for the final wicket.
Posting 68 in the first innings, Henriques became only the fourth batsmen to score a fifty in both innings on debut batting at number seven or lower, and will continue on Tuesday morning on 75.
Earlier, India's three tweakers, Ravichandran Ashwin, Harbhajan Singh and Ravindra Jadeja, demolished the Australian top-order.
Ed Cowan (32) and Phil Hughes (zero) fell within an over of each other, and Harbhajan picked up both David Warner (23) and an impatient Matthew Wade (eight) with straight ones.
Ashwin, who opened the bowling with fellow off-spinner Harbhajan, snared Shane Watson with the final delivery of the morning session.
Watson (17) played forward to a ball that was flighted outside off, but it dipped on him and found the shoulder of his bat for an easy catch by Virender Sehwag in the slips.
India batted for an hour on the fourth morning before they were dismissed for 572, securing a troublesome lead of 192 runs.
The hosts started the day on 515 for eight on a pitch that resembled a clay court, with Mahendra Singh Dhoni on 206 and Bhuvneshwar Kumar on 16.
The captain survived an early leg-before appeal from James Pattinson, but the quicky got his man in the sixth over of the day, after a change was made to the ball.
Bouncing the Indian skipper, Dhoni got inside the line, but gloved the ball through to Wade behind the stumps for 224 - eight runs short of the highest test score made by a wicketkeeper.
Nonetheless, the pair had done the damage with a ninth-wicket partnership of 140 that straddled two days.
Ishant Sharma kept Kumar company for 26 runs before the latter fell to a slower ball from Peter Siddle for a crucial 38 runs.
Pattinson bowled his heart out and deservedly finished with 5-96, his third career five-wicket haul.