Kolkata made 180-6 in their 20 overs after being put in to bat, opener Gautam Gambhir scoring 80, but the Super Kings reached their target with nine balls to spare and claimed the title for the second time.
The Knight Riders had won the Indian Premier League as they compiled a record winning sequence but their streak came to an end after 14 matches, despite a good start to the contest.
Robin Uthappa (39) and Gambhir put on 91 in less than 11 overs but Uthappa was then stumped by MS Dhoni off left-arm Pawan Negi, who went on to take 5-22 in an incredible spell.
Negi was playing in just his second match of the tournament but went on to remove Jacques Kallis (1), Manish Pandey (32), Ryan ten Doeschate (stumped for a first-ball duck) and Suryakumar Yadav (0).
And Gambhir hit three sixes and seven boundaries in his 52-ball knock before holing out off Ravindra Jadeja in the 17th over.
The Knight Riders were without banned spinner Sunil Narine but they removed Dwayne Smith (8) in the first over, clean bowled by Pat Cummins after hitting a pair of boundaries.
However, that brought Raina to the crease and he produced a superlative innings, treating Kolkata???s spinners with disdain as he marched out of his crease to hit big sixes.
He survived a stumping chance on 78 and Yusuf Pathan put down a very difficult caught and bowled opportunity when Raina had reached 88, but Chennai were firmly on top by this stage in any case.
Raina reached his third T20 century off 59 balls and finished with 109 not out off 62 balls, with six fours and eight sixes.
Opener Brendon McCullum (39 off 30 balls) played the junior role in a second-wicket stand which yielded 118 in 12.2 overs.
And Super Kings captain Dhoni then came in at number four to help guide the team to victory, finishing on 23 not out and hitting the winning runs.
Negi was named man of the match on the day while Raina was named player of the series.