Pune faltered in the death overs, leaking 63 runs in the last five overs with Henriques (55 not out from 28 balls) and Deepak Hooda (19 not out from 10) taking the bowlers to the cleaners.
Put into bat, Sunrisers had a slowish start with skipper David Warner and his opening partner Shikhar Dhawan (30) putting on 55 runs before South African leg-spinner Imran Tahir gave Pune the first breakthrough in the form of Dhawan.
The Pune bowlers started with a tight line and length and did not allow any freebies to the two left-handed openers.
Dhawan started his innings with a boundary off left-arm pacer Jaydev Unadkat and went on to smack four more before mistiming Tahir's first ball of the match and was smartly caught by Rahul Tripathi at deep midwicket.
Dhawan's departure brought in the in-form New Zealand skipper Kane Williamson (21 from 14 balls), who added 29 for the second wicket with Warner before medium pacer Daniel Christian's off-cutter caught him plumb in front.
Warner, at the other end, survived a chance when his Australian skipper Steve Smith put down an absolute sitter at mid-off off Ben Stokes.
But the joy was short-lived as the southpaw found the going tough after facing 43 balls for his 40 runs and fell to Unadkat in his attempt to switch hit a straight ball that crashed into his stumps.
Towards the end, Henriques and Hooda smashed some lusty hits over the rope to take the visitors past the 150-run mark.
Henriques started by hitting two consecutive fours off medium pacer Shardul Thakur before meting out special treatment to Unadkat for two sixes while Hooda too used the long handle once off Unadkat for a flat six into the second tier over long-on.
The right-handed Australian brought up his half century in the final over of the innings with a four into the extra cover boundary off Thakur.
Brief Scores: Sunrisers Hyderabad 176/3 (Moises Henriques 55 not out, David Warner 43, Shikhar Dhawan 30, Daniel Christian 1/20) vs Rising Pune Supergiant.