Ashwin wrought havoc on Australia's top order and some clever bowling ensured he claimed his sixth five-wicket haul in his 13th Test, although he was given precious little support as the tourists went to tea on 215 for five.
Australia opener David Warner lived a charmed life and eventually departed for 59, having been dropped twice, but Clarke (45 not out) and rookie Henriques (29no) put on a precious unbeaten 62 for the sixth wicket after Australia had limped to 153 for five.
India began the day by handing Harbhajan Singh his 100th Test appearance as well as giving seamer Bhuvneshwar Kumar his debut. Australia, after winning the toss, got off to a rollicking start with Warner and Ed Cowan scoring exactly 50 in the first 10 overs.
Warner was dropped in the ninth over, Ashwin's first, when he edged to Virender Sehwag at slip only to see a straightforward chance shelled.
Warner was handed another life when Mahendra Singh Dhoni failed to take a tough stumping chance off Ashwin - a failing he rectified when he whipped the bails off to remove Cowan for 29. Cowan had hit Harbhajan for the first six of the day moments earlier but was unable to repeat the dose against Ashwin and paid with his wicket.
The second wicket was soon to arrive, Phil Hughes lasting 15 uncomfortable balls for six before edging Ashwin onto his stumps with an ungainly cut.
Shane Watson brought up the Australia hundred in the 28th over, with Warner moving to 50 soon after with a well-run two. Both batsmen were to fall to Ashwin shortly after the lunch interval, however, with Watson dismissed for 28 after being trapped on the back foot, while Warner was deceived by a quicker delivery and he also departed lbw.
Ashwin had his fifth wicket when Matthew Wade played down the wrong line and was adjudged lbw to leave Australia reeling, but all-rounder Henriques showed maturity beyond his experience to help Clarke keep the score ticking over.
Australia's captain was given a lifeline shortly before the tea interval when umpire Kumar Dharmasena failed to spot an inside edge to short leg. Clarke duly struck his sixth four in the next over to move to within five runs of a half-century.