Put into bat, Kings XI Punjab piled up a mammoth 230 for 3 in 20 overs riding on Wriddhiman Saha's belliegerent unbeaten 93 off 55 balls.
In reply, Mumbai Indians nearly pulled off the highest ever chase in IPL before being restricted to 223 in 20 overs.
Needing 16 off the final over, Kieron Pollard (50 off 24 balls) saw one run being deducted off the first delivery as he didn't touch the crease at non-striker's end. The next delivery was pulled over sqaure leg for a six.
The win took Kings XI Punjab's points tally to 14 from 13 games and they still are in the hunt with a match against Rising Pune Supergiant left. Mumbai Indians have already qualified with 18 points and have a game left against Kolkata Knight Riders.
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The KXIP win also puts pressure on Sunrisers Hyderabad (15 points from 13 games) to win their last match to ensure smooth passage into last four.
Mohit Sharma, despite being smashed for 33 in his first two overs, bowled a delivery that climbed on a surging Parthiv, who offered simple skier to Manan Vohra.
Simmons, who scored his half-century off only 27 balls, hit five boundaries and four sixes, before a brilliant effort at the long-on boundary from Martin Guptill saw the Caribbean international head back to the dug-out.
Leg-spinner Rahul Tewatia then bowled a half-tracker to rival skipper Rohit Sharma (5), who provided the simplest of catches to Guptill at deep-mid-wicket.
The New Zealander was back in action when Nitish Rana (12) slogged one down his throat at the same position off Axar patel's bowling.
From 99 for no loss, Mumbai Indians slumped to 121 for 4 and it was a matter of time before scoreboard pressure got to the home team.
But Pollard and Hardik Pandya (30 off 13 balls) had other ideas as they smoked 55 runs in 3.3 overs to bring MI back in the game.
Earlier, Test specialist Saha displayed a different facet of his batsmanship with a stroke-filled unbeaten 93 of 55 balls to power Kings XI Punjab to 230 for 3.
Saha, who also has a century in the 2014 IPL final, struck 11 boundaries and three sixes to anchor the innings.
Martin Guptill hit a flurry of boundaries (5x4, 1x6) during his 18-ball-36 and skipper Maxwell's 47 off 21 balls also propped up the total. Maxwell's innings had five sixes apart from two boundaries.
Mitchell McClenaghan ( 1-54), Lasith Malinga (0-45), Harbhajan Singh (0-45), Jasprit Bumrah (1-24), Karn Sharma (1 -32 ) and Hardik Pandya (0-29) were hammered to all parts of the ground.
Before this, the highest total this season was 214 for 3 against Gujarat Lions.
Punjab were well-poised at 173/2 at the end of 15 overs and smashed 57 off last five overs to post the their overall highest score at the Wankhede.
The side has posted a total of 230 or above for the third time in all the 10 season of IPL.
Hardik Pandya conceded three fours in the opening over, two stuck by Kiwi Guptill and the other hit by Saha, who opened the innings in place of Manan Vohra.
Guptill was in his element hitting a towering six over long off Malinga. Saha struck two consecutive fours in the same over as Punjab reached 50 in only 3.4 just overs.
Guptill's departure did not bother Saha, as he continued to take on opposition bowlers, hitting two fours in the seventh over.
In the ninth over, off spinner Harbhajan was hit for three sixes by Maxwell.