Put into bat at Delhi's Feroz Shah Kotla, Hyderabad rode on Yuvraj Singh's 30-ball 44 to manage a respectable 162 for eight before restricting Kolkata to 140 for 8 wickets in 20 overs.
Medium-pacer Bhuvneshwar Kumar bagged three wickets as Australia's Henriques (2-17) and Hyderabad's star import from Bangladesh, Mustafizur Rahman (0-28) provided the adequate support.
Rahman was unable to get a wicket but his economical spell was instrumental in taking the David Warner-led side over the line.
Earlier the Hyderabad top-order fell to the guile of chinaman bowler Kuldeep Yadav, who got Man of the Match Henriques (31) and Warner (28) on consecutive deliveries.
Yuvraj then got the rebuilding act going with Deepak Hooda to stitch a 49-run fourth wicket partnership as the duo combined the right dose of caution and aggression.
The left-handed Yuvraj, who has represented India in 293 one-day internationals, struck eight fours and a six before being bowled by West Indies pacer Jason Holder.
Holder along with Morne Morkel shared two wickets apiece as the bowling duo complimented destroyer-in-chief Yadav (3-35).
Chasing what seemed a par score at the neutral venue, Kolkata lost a couple of early wickets but skipper Gautam Gambhir (28) kept chipping away.
Gambhir's wicket in the 10th over proved to be crucial as Henriques soon got dangerman Yusuf Pathan (2) back in the dug out with KKR in a tight spot.
Manish Pandey (36) and Suryakumar Yadav's 46-run fifth-wicket stand did raise hopes for a KKR recovery but Hyderabad bowlers kept getting wickets.
Hyderabad will now meet Gujarat Lions in Qualifier 2 in New Delhi on Friday to decide Royal Challengers Bangalore's opponent in the title clash Sunday. – AFP
Original source: Henriques helps Sunrisers sink KKR