Kolkata Knight Riders scored 149 for eight after being asked to bat first.
Venkatesh Iyer top-scored for KKR with 57 off 42 balls after openers Jason Roy (10) and Rahmanullah Gurbaz (18) could not convert their starts at the Eden Gardens, both falling to seasoned left-arm pacer Trent Boult.
In-form leg-spinner Yuzvendra Chahal finished with excellent figures of 4/25, continuing his fine run of form.
In reply, RR completed the chase in 13.1 overs. Sanju Samson smashed 48 off 29 balls.