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 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.
Henriques faced 124 balls hitting six fours and two huge sixes -- one each off Ashwin and Harbhajan. The Portuguese born all-rounder used his feet well against the spinner and also defended well when it mattered.
It was extremely frustrating final hour for the Indians as a desperate Dhoni in his bid to complete formalities finally brought Ishant Sharma in the 76th over of the innings but the pacer failed to break the partnership.
Earlier on, the troika of Ashwin, Harbhajan and Jadeja took full advantage of a crumbling pitch as the hosts reduced the Aussies to 128 for five at tea.
The spinners exploited the deteriorating conditions as they polished the Australian top-half in the post-lunch session as India looked to go for the kill.
Starting the post-lunch session at 34 for one, the Aussie batsmen found it difficult to play a surviving game on a pitch where there were enough footmarks on both sides for the spinners to trouble the batsmen.
Whenever the delivery landed on the rough, there was vicious turn on offer and also the variable bounce made life even more difficult.
Ed Cowan (32), who was trying to graft his way having played 97 balls, was finally adjudged leg before when an Ashwin delivery straightened after pitching and the left-hander wasn't entirely committed to the front foot. Although the batsman didn't look too happy, television replays suggested that the ball would have hit middle stump.
Phillip Hughes's nightmare ended in three balls as he got a delivery from Jadeja that nastily jumped onto him after hitting one of the spots. The ball ballooned off his gloves and Sehwag took the easiest of catches at slip.
Harbhajan, who had an indifferent first innings, bowled far better in the second essay. He was slower through the air and was also getting the required drift.
David Warner, who curbed his natural instincts to score a patient 23 off 61 balls, got a drifter from Harbhajan and was caught plumbed in front of the wicket.
Buoyed by the success, Harbhajan got his second wicket as he cleaned up Matthew Wade (8), who went for a wild sweep while completely missing the line of the delivery.
The final session also started on a bright note when Ashwin got one to turn sharply as Clarke was trapped on the backfoot with a ball keeping low.
With the departure of Australian captain, there were some premature celebrations in the stands.
While Henriques looked confident at one end, Peter Siddle was bowled by Jadeja to make it seven down.
However James Pattinson (11, 26 balls) provided some resistance which also helped Henriques to score a few runs in the process.
Finally, left-hander Pattinson became Ashwin's fourth victim in the second innings as he edged one to Sehwag in the slips. The senior opener took a judged catch low onto his left.
Mitchell Starc hit a couple of boundaries but didn't show intent to stay back for a long period as he tried to loft Ashwin to give an easy catch to Tendulkar in the long-on region.
Once Starc was gone, Australia still needed 17 runs to avoid the follow-on but Henriques and Lyon fought well to live for another day.