Australia was in a fair degree of strife at 5-153 when Indian off-spinner Ravi Ashwin claimed all five of the tourists wickets up to that point, but then Clarke and Henriques got together for an outstanding partnership of 151.
Their partnership puts Australia in a strong position at stumps on the first day at 7-316 with Clarke remaining not out on 103 and he has just been joined by Peter Siddle who is one.
Along the way to his century, Clarke reached 7000 runs in Test cricket and by reaching his ton did so for the 23rd time and continued his remarkable form since taking over as captain from Ricky Ponting.
It was also a tremendous performance from Henriques who was chosen to make his debut as an all-rounder ahead of Glenn Maxwell. The 26-year-old averages just 30.61 with the bat in 39 first-class matches but made a mockery of that with his 68 before he was out just before stumps.
Ashwin has been the star with the ball for India taking 6-88 from 30 overs.
Australia's openers started well enough with Ed Cowan and David Warner racing to 64 inside 15 overs after Clarke won the toss and elected to bat first.
The pace bowling pair of debutant Bhuvneshwar Kumar and Ishant Sharma were relatively easy to play on the spin-friendly wicket.
It didn’t take long for Indian captain MS Dhoni to bring on his spinners with Harbhajan Singh and Ashwin on to bowl though.
Cowan was just starting to look at home having hit four boundaries and a six on his way to 29, but was stumped by Dhoni off Ashwin.
Australia was 1-64 and then 2-72 when Phil Hughes played a poor shot to be bowled by Ashwin for six.
Shane Watson and Warner then put on 54 for the third wicket before just after lunch, Watson was trapped in front off Ashwin for 28. Warner was then gone to overs later in the same fashion off the same bowler for a well-made 59.
Australia was then in trouble at 4-131 and with Matthew Wade dismissed for 12, also LBW to Ashwin, the visitors were struggling at 5-153 before the outstanding partnership of 151 between Clarke and Henriques.
Henriques eventually fell for 68, also LBW to Ashwin, and Australia was then 7-307 just before stumps when Mitchell Starc was bowled by Ravindra Jadeja for three.