Batsman Suresh Raina was the hero, hitting an unbeaten 57, while skipper MS Dhoni struck 27 as the Super Kings rallied to 168-5 from their 20 overs.
Sachin Tendulkar led the chase with a battling 48, but the Super Kings fielded superbly in limiting the Indians to 146-9.
Domestically, centuries apiece from openers Andrew Gale (125) and Jacques Rudolph (101) helped Yorkshire to an emphatic 10-wicket win over Essex on the opening round of matches in the Clydesdale Bank 40 tournament. Gale smashed 12 fours and three sixes as the Tykes, who chased down Essex’s respectable 232-9 with 4.1 overs to spare.
Champions Sussex began their title defence with a five-wicket win over Worcestershire, while a boundary from Iftikhar Anjum with the penultimate ball secured Surrey a two-wicket victory over Lancashire.
England stars Jonathan Trott, Ian Bell and Jim Troughton all hit half-centuries to steer Warwickshire to a six-wicket win over injury-hit Kent.