After Shane Watson hit a blistering 80, Chennai needed two runs off the last ball to overtake Mumbai's 149-8. But the Sri Lankan veteran trapped Shardul Thakur lbw to claim the landmark win.
Malinga gave away 49 runs in his four overs but the last two overs by the Sri Lankan and fellow pace bowler Jasprit Bumrah, who took 2-14, were decisive.
The wicket extended the 35-year-old Malinga's record as the all-time best IPL bowler with 170 wickets from 122 games.
"About Malinga, that's what champions do," said Mumbai captain Rohit Sharma.
"I had confidence in him despite a poor third over. He also had confidence he could do it," Sharma said of his veteran paceman who is an expert at bowling yorkers in the death overs.
"I thought we could use Hardik Pandya for the 20th over, but I wanted to back someone who has done it for us and Malinga has been in that situation and done it."