Ravindra Jadeja produced a brilliant spell of spin bowling that saw him return figures of 4/12, after Brendon McCullum's sizzling half-century powered CSK to a daunting 148 for three. Mohit Sharma, too, bowled well bagging 3/22 for CSK.
In a match that was reduced to 17 overs per side after rain delayed the start by an hour and 40 minutes, CSK dominated throughout to post their fifth straight win in six outings. This was the Knight Riders' fourth loss after having started the first leg in the UAE with a bang.
The CSK bowlers, led by Jadeja, then combined to leave KKR gasping for breath at 38 for four in the sixth over.
Robin Uthappa top-scored for KKR with a 38-ball 47, while Yusuf Pathan made a 28-ball 41 with the help of four sixes and a four.
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To start with, in their chase, Kolkata were off with a flurry of boundaries, with most them coming from the blade of Uthappa, who hit Ishwar Pandey for two successive fours.
Gambhir was out after a confusion with his opening partner Uthappa. Hilfenhaus collected the throw from Dhoni and underarmed it to the stumps at the non-striker's end as the batsman failed to get back in time.
Kallis fell to an innocuous Ravichandran Aswhin delivery after he swept uppishly to the deep backward square leg fielder.
Manish Pandey was next to get out as he lobbed Jadeja's first ball into covers. Sharma then pulled off a good catch diving forward to send back Shakib Al Hasan and give Jadeja his second wicket.