With this win, Mumbai has now moved on to the third position in the league standings whereas Bangalore are languishing at the bottom.
Chasing a target of 172, Mumbai got off to a positive start as both openers Rohit Sharma and Quinton de Kock were at their fluent best, hammering the visitors for regular boundaries.
Mumbai was able to score 67 runs in the powerplay overs.
The duo stitched together a 70-run partnership before Sharma (28) was dismissed by Moeen Ali. The batsman failed to read the ball out the bowler's hands and he was bowled through the gate.
Ali dismissed de Kock (40) in the same over staging Bangalore's comeback in the match.
Suryakumar Yadav and Ishan Kishan retrieved the innings for Mumbai as they staged a quickfire 33-run partnership. Their resistance was ended by Yuzvendra Chahal as he defeated Kishan (21) in flight, getting him stumped. Krunal Pandya and Yadav put on a brief 25-run stand but Chahal once again provided the key breakthrough to Bangalore as he dismissed Yadav (29) in the 16th over of the innings, with Mumbai still requiring 43 runs for the win.
Hardik Pandya joined his brother Krunal in the middle and both these batsmen shrugged 19 runs from the remaining 43 runs, but Krunal was dismissed by Mohammed Siraj in the 18th over with the team still requiring 24 runs more.
The right-handed Pandya, however, kept on playing in his trademark style and he ensured Mumbai's victory by five wickets and with six balls to spare. Hardik remained unbeaten on 37.
Earlier, AB de Villiers and Moeen Ali's knocks of 75 and 50 respectively enabled Bangalore to post 171 runs on the board for the loss of seven wickets.
Bangalore got off to the worst start possible as they lost their skipper Virat Kohli (8) in the third over of the innings as Jason Behrendorff had him caught at the hands of the wicket-keeper, de Kock.
De Villiers and Parthiv Patel retrieved the innings for a while, stitching together a 37-run stand but Hardik dismissed Patel (28) in the seventh over reducing Bangalore to 49 for the loss of two wickets.
Ali, who came out to bat at number four started to play with an aggressive mindset and he, along with de Villiers gave the team much needed momentum in the innings. Both the batsmen mixed caution with aggression perfectly, allowing the team to gain some stability.
The duo shifted their gears in the latter part of the innings, hammering the hosts for regular boundaries. Both these batsmen stitched together a partnership of 95 runs which saw de Villiers and Ali bringing up their respective half-centuries in the 17th over of the innings.
The death over specialist Lasith Malinga staged Mumbai's comeback as he dismissed both Ali (50) and Stoinis (0) in the 18th over of the innings. De Villiers (75) was dismissed in the final over of the innings, as Keiron Pollard showed exceptional fielding skills to run the batsman out.
Malinga continued to strike in the final over, and his four-wicket haul helped Mumbai restrict Bangalore to just 171 runs in the allotted twenty overs.
Mumbai Indians will next play against Delhi on April 18 whereas Bangalore will face Kolkata on April 19.
With this win, Mumbai has now moved on to the third position in the league standings whereas Bangalore are languishing at the bottom