Pollard's blitz helped hosts Mumbai chase down their target of 198 on the final ball of the match and overshadow Punjab batsman KL Rahul's maiden century in the Twenty20 tournament.
The big-hitting Pollard, who captained the team in place of the injured Rohit Sharma, promoted himself to number four to produce his IPL best in front of a raucous home crowd.
Needing 15 for victory off the last six balls, Pollard got out on the second delivery as fellow West Indian Alzarri Joseph completed the chase with an unbeaten 15.
Pollard lifted his side from 62-3 after nine overs to single-handedly revive Mumbai's hopes. His 54-run seventh wicket stand with Joseph stood out.
"I went up the order because I enjoy batting at Wankhede (Stadium)... (It) was a difficult pitch to bowl on and good to bat on," said Pollard, who hit three fours and 10 sixes.
"We did well with the ball after the start they got. We did pull things back in the middle overs a bit but lost the plot at the end.
"Again, can't be harsh on the bowlers. We finished on the right end of the result and thanks to God for that too," he added.
Earlier, Rahul hit 100 off 64 deliveries to guide Punjab to 197 for four after being put into bat first.
Rahul's innings came at an opportune time for the opener with the Indian selectors scheduled to announce the team for the 50-over showpiece event on Monday.
Rahul, who has two international T20 hundreds, put on 116 runs with opening partner Chris Gayle, who hit 63 of 36 deliveries to lay the foundation of their team's 197-4.
Gayle and Rahul took apart the Mumbai bowlers after being put into bat first, scoring 50 runs for Punjab in the first six overs.
"I like him as a batsman. He has got great technique, he has got a lot of style," West Indian batting great Brian Lara said on Star Sports.
"Chris Gayle got out and he knew he had to bat till the end. To get a hundred in an IPL game is amazing. I Just love the way he bats and I can watch him bat every single day."
The left-handed Gayle fell to paceman Jason Behrendorff in the 13th over and Hardik Pandya struck back with two more wickets.
But Rahul had other ideas as he launched an assault in the final three overs that got Punjab 54 runs, including 25 from Pandya's penultimate over.
Rahul, who recently admitted to having doubts about himself after a sexism storm involving him and Pandya earlier this year, hit six fours and six sixes as he surpassed his previous IPL best of 94 in the final over.
He is only the fourth batsman this IPL season so far to score a hundred after Sanju Samson of India, England's Jonny Bairstow and Australian David Warner.