Henriques batted patiently to take the visitors to 215 for five at tea on the opening day of the first cricket Test, in Chennai on Friday.
Harbhajan Singh being greeted by BBCI president N Srinivasan for his 100th Test appearance during the first Test match between India and Australia at MA Chidambaram Stadium in Chennai. (PTI)
Ashwin added three quick wickets in the post-lunch session to reduce Australia to 153 for five but Clarke and debutant Henriques denied India any further leverage, handling the spin attack quite confidently.
Clarke was bating on 45 and Henriques was giving him company on 29 when the players took break.
Clarke brought in all his experience of playing in the sub-continent as his footwork was splendid while negotiating the turning balls.
He got good support from Henriques, who did not fear to play chip shots by stepping out to spinners, never allowing Indians to dominate or take advantage of a fast wearing track.
Australia added 89 runs in the session while India took three wickets, all claimed by Ashwin.
Ashwin yet again was the most impressive of the Indian spinners as his bowling had all the ingredients -- turn, bounce and zip -- to trouble the batsmen.
All his three victims were trapped before the wicket as he dismissed Shane Watson (28) David Warner (59) and wicket-keeper Matthew Wade (12).
The three strikes in a space of 10 overs pegged Australia back as they had started the second session on a healthy 126 for two but Clarke and Henriques remain unseparated after that, sharing a 62-run stand for the sixth wicket.
Clarke was lucky to stay at the wicket as umpire Kumar Dharamsena turned down a close-catch appeal off Ashwin, 10 minutes into the tea break.
TV replays suggested that the batsman had indeed edged the ball before it flew into the hands of forward short-leg fielder. He was on 39 at that time.
Australia: Ed Cowan, David Warner, Phil Hughes, Shane Watson, Michael Clarke (captain), Matthew Wade (wicketkeeper), Moises Henriques, James Pattinson, Mitchell Starc, Peter Siddle, Nathan Lyon. 12th man: Glenn Maxwell
India:Virender Sehwag, Murali Vijay, Cheteshwar Pujara, Sachin Tendulkar, Virat Kohli, Ravindra Jadeja, Mahendra Singh Dhoni (captain/wicketkeeper), Ravichandran Ashwin, Harbhajan Singh, Bhuvaneshwar Kumar, Ishant Sharma
(With PTI and IANS inputs)