KKR skipper Gautam Gambhir and Jacques Kallis added 43 runs for the second wicket to lay a solid foundation.
Gautam Gambhir was the top-scorer for KKR, scoring 53 off 45 balls.
Eoin Morgan provided Kolkata the push they needed in the final overs to reach 180 for 4. Morgan scored 47 off just 21 balls before being run out by Dale Steyn.
KKR's Jacques Kallis followed up his 27-ball 41 with an effort of 3 for 13 with the ball. (BCCI Image)
Hyderabad allrounder Thisara Perera staged a mini fightback but it ended at 36 off 25 balls when Kallis bowled him. (BCCI Image)