Chasing 172 for a win, the match was in a balance when he came out in the 16th over but Hardik, who was named in India's World Cup squad on Monday, turned the game on its head, smashing five boundaries and two sixes during his unconquered 16-ball innings on a turning track at the Wankhede Stadium.
Mumbai needed 22 runs from the last two overs but Hardik took just six balls to hit the required runs, smashing left-arm spinner Pawan Negi for two boundaries and as many sixes to end the run chase.
He finished the game with a single off the last ball of the 19th over as Mumbai reached 172 for 5 in 19 overs.
Mumbai were off to a flying start in their run chase with openers Rohit Sharma (28) and Quinton de Kock (40) finding the boundaries with ease.
De Kock took 16 runs from the third over bowled by Umesh Yadav, smashing two boundaries and a six while captain Rohit was elegant as ever, hitting a four and a six off Mohammed Siraj the next over.
Mumbai were wallopping at 67 for no loss at the end of first powerplay overs but suddenly off-spinner Moeen Ali (2/28) brought RCB back into the match with a two-wicket burst in a single over.
This was Mumbai's fifth win in eight games and they are now at third spot with 10 points, while RCB suffered their seventh defeat in eight matches and the Virat Kohli-led team are languishing at the bottom of the table.
Earlier, veteran Sri Lankan pacer Lasith Malinga took four wickets for 31 runs as Mumbai restricted RCB to 171 for 7. Mumbai were off to a flying start in their run chase with openers Rohit Sharma (28) and Quinton de Kock (40) finding the boundaries with ease.
Earlier, AB de Villiers and Moeen Ali hit impressive half-centuries to guide Royal Challengers Bangalore to a respectable 171 for 7 after being put into bat.
After RCB lost skipper Virat Kohli (8 off 9 balls) and Parthiv Patel (28 off 20 balls) inside seven overs, de Villiers (75 in 51 balls) along with Ali (50 runs in 32 balls) resurrected the innings with a 95-run stand for the third wicket.
Ali initially played second fiddle but later upped the ante. He was particularly severe on Australian pacer Jason Behrendoff (1/49), whom he hit for two sixes and a four in the 16th over, which fetched 17 runs for RCB.