The Sri Lanka fast bowler proved more than useful with the bat as he scored 37 from 18 balls late in the match to defeat the defending champions by three wickets.
Chennai batted first and raced to an impressive 157 for four from their 20 overs, aided by 81 from the opening batsman Michael Hussey.
But Malinga and Harbhajan Singh fought back with an unbeaten last-wicket stand of 53 to squeeze past the target with one ball remaining.
Hussey had put Chennai in control after they won the toss and decided to bat, hitting three sixes and eight fours in his confident innings before his wicket fell with the score on 144.
Suresh Raina went for 18 from 17 balls, stumped off the bowling of Kieron Pollard, before the new batsman, Subramaniam Badrinath, survived a run-out attempt when he had scored three after replays showed he grounded his bat just in time.
In the earlier Champions League match yesterday, Cape Cobras cruised to a seven-wicket victory over New South Wales. Chasing just 136 for victory, the former South Africa opener, Herschelle Gibbs, was the standout performer, scoring a 47-ball 55 for the Cape Cobras.