Play was called off because of rain when the Knight Riders were 61 for two at the end of 10 overs while confidently chasing 115 for victory on a sticky Eden Gardens pitch. They were declared winners on the Duckworth/Lewis method as they were ahead at the halfway stage of their innings.
Opting to bat, Super Kings made 114 for four after the start was delayed by an hour due to rain.
Kolkata joined Mumbai Indians on top of the IPL standings, with Chennai two points behind. Mumbai were playing Delhi Daredevils later.
A fighting 54 by Subramaniam Badrinath helped Chennai pass 100 runs on a low, slow pitch following a controlled bowling display by Kolkata.
Badrinath struck the first boundary of the innings in the 10th over and put on 65 for the fourth wicket with Albie Morkel, who scored 30.
Chennai offspinner Ravichandran Ashwin dismissed Kolkata's Eoin Morgan for 5 and Gautam Gambhir for 16 but South African Jacques Kallis and in-form Manoj Tiwary were batting fluently on 21 and 15 when rain stopped the match.
Kolkata left-arm spinner Iqbal Abdulla, who took 1-15 off four overs, was declared man of the match.
Brief scores: Kolkata Knight Riders 61-2 in 10 overs (Ravichandran Ashwin 2-12), def. Chennai Super Kings 114-4 in 20 overs (Subramaniam Badrinath 54, Albie Morkel 30 not out) by 10 runs on D/L method.