Josh Inglis and Marcus Stoinis played their parts on the pitch for the Ricky Ponting-coached Kings, who set up a tantalising final with the Virat Kohli-led Royal Challengers Bengaluru.
The result means Tuesday's decider at the same venue will crown a new IPL champion, with Bengaluru, who feature another Aussie in Josh Hazlewood, also falling short in the summit clash in 2009, 2011 and 2016.
Punjab lost to Bengaluru in the first playoff match on Thursday, but they will now have another shot at winning their maiden trophy.
Shreyas Iyer played a captain's knock for the Kings, who had won the toss and opted to field before the rain came down and delayed Sunday's start to the game by more than two hours.
But they did not lose any overs, with the match at the Narendra Modi Stadium in Ahmedabad eventually finishing at well past 1.30am local time.
Chasing a target of 204 for victory, Iyer smashed an unbeaten 87 off 41 balls as his team returned to the final for the first time in 11 years.
"I love big occasions. I always tell my team, the bigger the occasion, the calmer you are," said Iyer, who captained Kolkata to the title last year before moving to Punjab.
"We shouldn't think about where we went wrong (against Bengaluru) because throughout the season we've been playing amazing ... One match cannot define us as a team."
Stoinis, who earlier took 1-14 in his only over the match, was unbeaten on two at the finish with Iyer, while Inglis contributed 38 runs. His 21-ball cameo included five boundaries and two sixes.
Punjab had a good start when Rohit Sharma fell cheaply in the third over but Jonny Bairstow (38) and Tilak Varma (44) went after the bowling before Suryakumar Yadav smashed three sixes and four boundaries in his quick-fire knock of 44.
A mammoth total looked on the cards but Yuzvendra Chahal and Azmatullah Omarzai picked up two wickets, including skipper Hardik Pandya, to restrict Mumbai to 6-203.
In response, Punjab scored 64 runs in the powerplay with Inglis leading the charge before Iyer and Nehal Wadhera stitched together an 84-run partnership for the fourth wicket to frustrate Mumbai.
Wadhera fell for 48 but Iyer notched up his half-century in 27 balls.
Iyer took a liking to Ashwani Kumar, hitting a high and handsome six before clearing the ropes three more times in the 19th over which went for 26 runs and Punjab won with an over to spare.
"The way he batted, he took his chances. Some of the shots he played were really outstanding," a bitterly disappointed Hardik said.
With AAP.
