Rahul and Finch took Mayank Markande's third over, the 16th of the innings, for 18 runs.
Tye raised his IPL-leading wickets tally to 24, becoming the first bowler in the competition's history to snare three four-wicket hauls in one season.
Andrew Tye does not come across as an angry 31-year-old.
In his next over, the last of the PowerPlay, Tye struck off successive balls to reduce Mumbai to 60 for three. Punjab who once led the table, have now slipped to the 6 spot and they have to depend on other teams after winning their last fixture against SunRisers Hyderabad. You know, in the first few games we have KL, [Chris] Gayle or Karun [Nair] who'd scored half-centuries or a century. He then took 17 runs from the following over sent down by Aussie Marcus Stoinis. Jasprit Burma, Man of the Match in Mumbai's win for taking three wickets, made a significant jump to fourth place on the bowling table and now has 16 wickets.
"You always want to bowl a good over but some days, it doesn't go your way because at the position where I bowl, it is hard, especially at this ground with the dew around", added Bumrah, who rediscovered his form after finishing with 1-19 against Punjab at Indore on May 4.More news: Wall Street heads south as Trump bashes China and oil prices flare
From 79/4 at the halfway mark - when two floodlight towers at the Wankhede dozed off - Mumbai Indians upped the ante to add 107 in their final ten overs.
When the former was reintroduced in the 17th over, skipper Ashwin had already broken the risky stand in the previous over, accounting for Pollard.
Batting first, MI did not have a great start, with Evin Lewis (9) getting out early. And when Rohit Sharma's mistimed pull found mid-on, Mumbai were caught in an awkward position at 71 for 4 in the ninth over.
Middle-order batsmen Axar Patel (10 not out), Yuvraj Singh (1) and Manoj Tiwary (4 not out) tried to reach the target but failed.
Keeping with Mumbai's modus operandi, Krunal Pandya and Pollard too showed no inclination to take their innings deep.
IPL 2018, Mumbai Indians vs Kings XI Punjab at the Wankhede Stadium, latest update and cricket scores: KL Rahul is ensuring KXIP are well in it. "As good as our bowling attack is, we have not been putting up complete performance as a team with both bat and ball and that sums up why we have not won games lately", he said.