Sri Lankan Malinga grabbed his season's best four for 23, including three wickets in his last over, while New Zealander Mcclenaghan picked up three for 20 that included top scorer Shikhar Dhawan's scalp, to restrict the Sunrisers to 137 for eight, chasing a target of 158.
The Sunrisers lost their way after a brisk opening stand between left-handers Dhawan, who top-scored with 42 off 29 balls, and David Warner (9).
Once these two departed within a short span to leave the Sunrisers reeling at 52 for two in six overs, the other batsmen did not prove to be good enough.
Earlier, electing to bat, MI rode on opener Lendl Simmons's 51 off 42 balls and some useful contributions from skipper Rohit Sharma (24) and West Indian Kieron Pollard (33) to reach a total of 157 for eight.
The victory, which was only their second of the season in seven games, helped MI stay afloat in their quest to reach the play-offs. This was Sunrisers fourth defeat in six games.
Chasing the target, the visitors set off to a fine start with Dhawan scoring at a fast pace. From the moment he caressed Harbhajan Singh's first ball of the innings to the cover fence, he looked in fine nick.
The left handed Indian opener later struck Harbhajan for three fours and a six in the bowler's second over to banish the offie from the attack.
Warner, watching from the other end, also hit Harbhajan for a four but then holed out to third man off a short ball from Malinga.
Then Dhawan departed while pulling Mitchell McClenaghan to short mid-wicket.
MI sensed a whiff of a chance with the visitors at 52 for two at the end of powerplay and applied pressure on new batsmen Lokesh Rahul and Naman Ojha with some tight bowling and sharp fielding.

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