Chasing 152 for a win, Pollard and Buttler smashed unbeaten cameos of 35 and 29 respectively to share 55 runs from just 3.3 overs for the unbroken fifth wicket to take Mumbai home with eight balls to spare at the Chinnaswamy Stadium.
Pollard smashed three fours and two sixes in his 19-ball unbeaten innings while Buttler hit one four and three sixes in his 11-ball unconquered knock as the duo struck a flurry of fours and sixes towards the end to take Mumbai home.
Bangalore kept themselves into the match with some brilliant fielding as Stuart Binny and AB de Villiers took a stunning catch each but in the end the score they defended was found to be too small.
Buttler hit the winning runs, a six, as Mumbai reached 153 for four in 18.4 overs to notch up their sixth win in 11 matches and jump to the fourth spot in the league table with 12 points.
Bangalore, on the other hand, slumped to their sixth loss in 10 matches as they remained at sixth spot with eight points. They will now need to win all their remaining matches to have a chance of making it to the play-offs stage.
Mumbai had captain Rohit Sharma at the other end and along with Rayudu steadied the innings with sensible batting.
(REOPENS DEL82)
Rohit's dismissal somewhat changed the scenario as the asking has reached near 10 an over by then. Binny then took a stunning catch near the boundary ropes to dismiss debutant Nitish Rana (9) of the bowling of Yuzvendra Chahal to leave Mumbai at 79 for 3 in the 13th over.
Pollard and Buttler, however, kept their cool as they took 18 and 16 runs in the next two overs with a flurry of fours and sixes off Shane Watson and Chris Jordan to ease off the pressure.
Mumbai needed just 10 runs from the final 12 balls and Buttler ended the match early by hitting a six in the fourth ball of the penultimate to take Mumbai home.
The Bangalore top order batsmen, except for Rahul (68 not out), failed to click after being put into bat but a late flurry of lusty blows from the wicketkeeper batsman saw the home side reach to a fighting total.
Rahul, who came in when Bangalore were in a precarious 17 for two in the fourth over, struck three fours and four sixes in his 53-ball unbeaten innings.
He shared 43 runs with AB de Villiers (24) for the third wicket and another 53 with Sachin Baby (25 not out) for the unbroken fifth wicket as the home side went past 150-run mark on account of the late recovery.
The cause of the home side was helped by the 23 runs Kieron Pollard leaked in the 18th over with Sachin Baby hitting two sixes and a four while Rahul also his share of a maximum hit.
For Mumbai, Mitchell McClenaghan, Tim Southee and Krunal Pandya took a wicket each.
Bangalore captain Virat Kohli (7), who has been in red hot form, met with a rare failure of the season. He struck a six in the fifth ball of the match bowled by Southee but was dismissed in the second over by Mitchell McClenaghan.
Two overs later, Chris Gayle (5) perished as he tried to smash a back of a length delivery on the off bowled by Southee with Rohit Sharma taking a well-judged catch.
AB de Villiers (24) and Shane Watson (15) got the starts but could not convert on them.
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