Michael Hussey made a dashing 59-ball 95 that guided Chennai to a formidable 200 for three in 20 overs and helped them to win.
Hussey also ran out a rampaging Mavinder Bisla (92) that saw Kolkata Knight Riders managing 186 for four in 20 overs.
Knight Riders skipper Gautam Gambhir's decision to field backfired right from the start as Hussey and Wriddhiman Saha (39) added 103 runs for the first wicket to set the foundation for the huge total.
Runs were flowing from both the ends and Gambhir in a desperate measure used seven bowlers within 10 overs.
Hussey and Saha played with ease. Hussey was the first to go after the Knight Riders' bowling and Saha took on his statemate Shami Ahmed, smashing him for two fours and a six as 15 runs came from the fourth over.
The team's 50 came up in the sixth over as both Hussey and Saha plundered the veteran Jacques Kallis for 18 runs in the sixth over.
It was medium pacer Rajat Bhatia, who broke the partnership by getting rid of Saha, who struck four fours and two sixes in his 23-ball knock.
Just when it looked that Hussey would get his maiden IPL century and third of the season, he holed out to Debabrata Das in deep midwicket off Sunil Narine. Hussey struck 11 fours and two sixes in his 59-ball knock.
Suresh Raina (44) and Mahendra Singh Dhoni (18 not out) hit a few lusty blows as 200 came up easily.
While chasing, Kolkata were in deep trouble after they lost Gambhir (14) and Brendan McCullum (4) cheaply for just 63 runs on board in the sixth over. Runs were simply hard to come.
Bisla played a brilliant innings of 61-ball 92 hitting 14 fours and two sixes that got Knight Riders close. They got 79 runs in the last seven overs but still it was too much of a task. Eoin Morgan remained unbeaten on 32.
In the last over, Kolkata needed 18 runs but Chris Morris bowled well giving away just four runs.