Rahul, who was suspended and ordered to leave tour of Australia in January with teammate Hardik Pandya over sexist remarks, struck an unbeaten 100 off 64 balls.
He smashed 54 from the last three overs, including 25 off one from Pandya, but his effort was in vain with Pollard striking 83 off just 31 balls as Punjab went down to Mumbai Indians by three wickets.
Rahul's knock comes at an important time with the Indian selectors scheduled to announce their squad for the World Cup on Monday.
Rahul is now the fourth batsman this IPL season so far to score a hundred after Sanju Samson, Jonny Bairstow and David Warner.
"I like him as a batsman. He has got great technique, he has got a lot of style," said West Indies batting great Brian Lara while commentating 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."
Rahul, who has two T20I hundreds to his name, put on 116 runs with opening partner Chris Gayle, who hit 63 off 36 deliveries to lay a solid foundation for their side.
Mumbai's stand-in-skipper Kieron Pollard struk 83 off 31 balls to help his team chase down their 198-run target on the last ball.
With Mumbai needing 15 to win off the final over, Pollard was out on the second delivery with fellow West Indian Alzarri Joseph completing an astonishing run chase.