Posing a competitive 167 runs for the loss of seven wickets, KKR bowlers restricted the oppoents at 132 for nine in their 20 overs.
Except Moises Henriques (41), none of the Sunrisers batsmen contributed much with their willows.
Skipper David Warner, who had been showing good form so far in the tournament, departed after making just four runs.
Umesh Yadav and Brad Hogg have picked up two wickets each for KKR.
Earlier, Robin Uthappa (30), Gautam Gambhir (31), Manish Pandey (33) and Yusuf Pathan (30*) contributed with their willows to post 167 runs on the scorecard.
Bhuvneshwar Kumar and Karn Sharma picked up two wickets each.
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