Put into bat, Chennai amassed 192-3 with opener Faf du Plessis anchoring their innings with 86 off 59 balls, which also earned the South African the man-of-the-match award.
Opener Ruturaj Gaikwad made 32 and went on to claim the orange cap as the tournament's leading scorer.
Robin Uthappa (31) and Moeen Ali (37 not out) chipped in with useful cameos to help Chennai post an imposing total at the Dubai International Stadium.
Kolkata, led by England white-ball captain Eoin Morgan, got off to a flying start with openers Shubman Gill and Venkatesh Iyer smashing individual fifties.
Gill made 51 and Iyer scored 50 before wheels came off their innings and two-time champions Kolkata, cruising at 91-0 in the 11th over, eventually finished on 165-9.
Shardul Thakur (3-38) dismissed Iyer and Nitish Rana in the same over, and left-arm spinner Ravindra Jadeja also bowled a two-wicket over to rip the heart out of Kolkata's middle order.
All-rounder Jadeja also took two stunning catches in the deep as Chennai, who missed the playoff for the first time last year, went on to claim the title.
"It was important to take responsibility and we had match-winners coming game after game and performing.
"People who were in form, they made sure they were scoring throughout the tournament, and everybody else was chipping in."
Morgan scored four as his lean run with the bat continued ahead of the Twenty20 World Cup beginning on Sunday.
"Our guys fought incredibly hard and performed but today, unfortunately, proved just one game too many," said the England captain.
The second half of this year's IPL was shifted to the United Arab Emirates following a COVID-19 surge in India.