Left-arm chinaman bowler Kuldeep returned with figures of three for 35 to deny Sunrisers a huge total and was ably supported by Morne Morkel (2/31) and Jason Holder (2/33).
Sent into bat, Sunrisers were dealt a big blow when Shikhar Dhawan departed in the last ball of the second over.
Dhawan started on a bright note and struck Morkel for back-to-back boundaries before perishing in search of one too many as the South African pacer went through his defence.
Henriques (31 off 21 balls) became Kuldeep's first victim as the batsman gave a straight forward catch back to the bowler in search of a big shot just after clobbering him over long-off for a six and then Warner was bowled in the very next ball as Sunrisers slumped to 71 for three after 10 overs.
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Sunrisers opened the floodgates in the 13th over when Yuvraj Singh (44 off 30) lofted Kuldeep straight over the head for a four and a six.
Sunrisers promoted big-hitting Ben Cutting up the order ahead of Naman Ojha but the Australian failed to make any impact as he was foxed by a googly from Kuldeep and Robin Uthappa did the rest behind the stumps.
But Yuvraj looked in vintage touch as he hit the bowler for consecutive fours in 17th over to take Sunrisers forward.
Towards the end, Bipul Sharma (14 not out off 6) played a short cameo as he walloped Morkel for two hits over the fence in the final over to take Sunrisers past the 160-run score.