Chasing a modest 161, the Knight Riders reached the target in 16.2 overs, losing just three wickets in the process at the Eden Gardens.
The Kolkata outfit rode on half-centuries by skipper Gautam Gambhir (71 not out) and Robin Uthappa (59).
For Delhi, Kagiso Rabada chipped in with two wickets for 20 runs.
Earlier, sent in to bat, Delhi opener Sanju Samson top- scored with a blazing 60 off 38 balls, while Shreyas Iyer contributed with 47 off 34 balls.
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