Mumbai were struggling at 59 for four in the ninth over when Pollard came to the crease and the West Indian bailed his side out of troubled waters with his 38-ball knock.
Pollard's innings was studded with nine boundaries including five sixes and he single-handedly brought his side back in the match even as Dinesh Karthik contributed 37 runs.
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Mumbai scored 52 runs in the last five overs as Pollard and Harbhajan Singh shared an unbeaten 65-run stand for the seventh wicket. Harbhajan scored a run-a-ball 21.
Dwayne Bravo (2/44) scalped two batsman while four other Chennai bowlers took a wicket each.
Mumbai lost both the openers inside the first 20 balls with Sachin Tendulkar getting a first ball duck in the fifth ball of the first over and skipper Ricky Ponting becoming victim of IPL debutant Ankit Rajpoot.
Dirk Nannes gave Mumbai a big jolt when he trapped Tendulkar, who played across the line and was caught plumb.
Ponting was a bit early into his pull shot and the leading edge was taken by R Ashwin at first slip. It was a big wicket for the 19-year-old UP paceman Rajpoot to start off.
Mumbai survived more damage when Rajpoot grassed Rohit Sharma (8) off Nannes but the batsman finally walked when M S Dhoni held a thin edge, induced by Dwayne Bravo.
In between Suresh Raina failed to hold on to powerful cut shot by Dinesh Karthik, who responded with a six off Rajpoot the next ball and kept hitting boundaries to ensure that his side keeps a decent run rate.
It was important for Mumbai that Karthik (37) stays and play a good knock but Barvo returned for his second over and trapped the diminutive batsman.
In came Pollard and he smashed Bravo to two consecutive boundaries. Despite losing wickets intermittently, Mumbai were managing a decent run-rate of seven.