Mumbai have 16 points from 13 outings and have a game left on Sunday against Kolkata Knight Riders, while Sunrisers are placed fourth with 12 points.
Hyderabad needed 17 runs off the last over and the equation was brought down to seven by the time Hardik braced up to bowl the final delivery.
But Manish Pandey (71 not out off 47 balls) carted the all-rounder over long-on for a six to bring the scores level and force a Super Over, a first at the Wankhede.
Chasing 163, Hyderabad needed 41 runs from 18 balls, but Malinga (0-37) conceded 12 runs as the equation was brought down to 29 runs off 12 balls.
Then Bumrah (2-31) gave 12 runs in the penultimate over, with Manish Pandey hitting two fours.
Earlier, Quinton De Kock’s unbeaten 69 took the hosts to a respectable total on a difficult pitch.