Chasing the visitors' total of 178 for 7, built mainly around Manish Pandey's swashbuckling 47-ball 81, MI got off to a superb start before losing four wickets in a cluster and looked down in the dumps at 119 for five before pulling off the win in 19.5 overs.
The heroes of MI's thrilling run-chase were one-down batsman Nitish Rana, who kept them in the hunt when wickets fell around him to make a 29-ball 50, and Hardik Pandya who cracked an 11-ball 29 to clinch a thrilling win.
MI needed 49 runs off the last three overs and the 18th over by Boult swung the game their way as he was hit for two sixes, one each by Rana and Pandya, conceding 19 runs that brought down the run rate.
Although Rana departed in the penultimate over from Ankit Rajpoot after reaching his 50 in 28 balls, Pandya struck Rajpoot for a six to bring down the equation to eleven from six balls.
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In the Mumbai run-chase, openers Parthiv Patel (30) and Jos Buttler (28) put on 65 runs before the partnership was broken in the 8th over by Chinaman bowler Kuldeep Singh who trapped left-handed Patel in front.
Mumbai, then, lost the wickets of Buttler and captain Rohit Sharma, who were both declared out leg before off a full toss and a clear inside-edge respectively by Ankit Rajpoot and Sunil Narine.
And when Krunal Pandya was caught behind to a leg side deflection, MI were left struggling at 97 for four in the 13th over.
Rana smacked Kuldeep for a six and a four in successive balls while the big-made Kieron Pollard pulled Rajput from wide of stumps over the mid-wicket to keep the hunt on as MI crossed 100.
Earlier, Pandey smashed five sixes and as many fours to blitz his way to an unbeaten 81 and help the Knight Riders recover from a mini collapse and muster a challenging score.
The visitors, asked to bat first, made a brisk start when openers Chris Lynn (32) and captain Gautam Gambhir (19) put on 44 runs in four overs before losing their way against left arm spinner Krunal Pandya.
Krunal's twin strike in the fifth over reduced the Knight Riders from 44 for no loss to 48 for two and then 87 for four before the innings was revived by Pandey's 47-ball innings.
It was mainly due to the Karnataka batsman's clean hitting that the total crossed the 150 mark.
But apart from his superb innings and opener Lynn's 24-ball 32, the innings lacked character.
Krunal finished with fine figures of 3 for 24 while Malinga got 2 for 36 while McClenaghan finished with 1 for 51.
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