Chasing 218, MI got off to a flying start with openers Rohit Sharma and Quinton de Kock adding 71 in 7.4 overs. However, three quick wickets brought CSK back into the match.
Pollard then took charge and hammered the bowlers into submission.
He added 89 for the fourth wicket with Krunal Pandya (32 off 23 balls) and got to his fifty in just 17 balls.
Mumbai needed 16 runs in the final over and Pollard smashed two fours and a six before running two off the last ball to seal the game for his side.
Earlier, CSK posted a massive 218/4 riding on an unbeaten 72 off 27 balls by Ambati Rayudu.
Rayudu added an unbeaten 102 (off 49 balls) with all-rounder Ravindra Jadeja (22 not out off 22 balls).
Brief scores: Chennai Super Kings 218/4 in 20 overs (A Rayudu 72 not out, M Ali 58, F du Plessis 50, K Pollard 2/12) vs Mumbai Indians 219/6 in 2 overs (K Pollard 87 not out, Q de Kock 38, S Curran 3/34).