Australia's 84-over second innings has included only three overs of pace bowling from Ishant Sharma as Ashwin and fellow spinners Ravindra Jadeja (2-68) and Harbhajan Singh (2-55) exploit the crumbling red-clay pitch.
The tourists have only one frontline spinner and offspinner Lyon had a difficult first innings, conceding 3-215.
But Henriques says Lyon and Australia's pace attack are confident they can put India's batsmen under pressure, even with only a small total to defend.
"MS Dhoni was able to put on 100 or 150 (140) with the guy batting at 10, so if we come out tomorrow you just never know, especially on a day-five wicket," Henriques said.
"Our backs are up against the wall.
"We know that especially on a wearing wicket, it's only going to get tougher to start (for India's batsmen).
"It's that type of wicket where you almost have to concentrate as if every ball is your first one because you have to stay sharp and make sure you're alert for that one that does act a little differently.
"Sometimes you will get one that you just can't do anything about."
India had resumed on 8-515 and were all out for 572, boosted by Dhoni's 224, a record for an India captain.
He was one of five victims for Aussie quick James Pattinson (5-96).
Australia's top order of Ed Cowan (32), Shane Watson (17) and David Warner (23) failed to capitalise on their starts while Phil Hughes (0) at No.4 and Michael Clarke (31) were victims of a couple of sharp-turning deliveries.
Opener Warner batted at No.3 after a bout of gastro.
Matthew Wade (eight) was bowled attempting a slog-sweep shot against Harbhajan and Peter Siddle (two), Pattinson (11) and Mitchell Starc (eight) went cheaply before Australia's fightback late on Monday.
Meanwhile, team doctor Peter Brukner announced that reserve quick Jackson Bird would be sent home for precautionary scans on a back injury.
-AAP
