Captain Cameron White and Hanuma Vihari scored 43 and 41 respectively while opener Shikhar Dhawan smashed a quickfire 59 as the Sunrisers mustered 178 for three off their 20 overs.
Lasith Malinga starred with the ball for Mumbai as the Sri Lankan paceman took two for 26 from his four overs, and it set up an enthralling chase for the hosts.
With nearly nine runs per over required, Sachin Tendulkar led the way opening the innings with West Indies batsman Dwayne Smith, but the Indian legend was forced to retire hurt with 38 runs to his name.
Number three Dinesh Karthik scored 30 runs off 23 balls to settle the hosts down alongside Rohit Sharma, who was left not out on 20 having consolidated effectively for the Indians.
But it was the explosive Kieron Pollard of the West Indies whose belligerent hitting ensured the victory for Mumbai as he blasted an unbeaten 66 off just 27 balls as his side reached their target with three deliveries remaining.
Such was the ferocity of Pollard’s hitting that a staggering 36 runs were racked up in the space of just seven deliveries as the muscular batsman took the match away from a shellshocked Hyderabad.
Man of the match Pollard said: "I didn't have any breakfast today, I woke up 1am. It was an important game for us, I backed myself, it's just a matter of chasing the right bowler, Perera was the unlucky one.
"I haven't fired only in the last couple of games, but I am a power hitter and I love to bat as well. You have to take the good times, and the bad times."
The victory - Mumbai's 10th from 14 matches - sees Sharma's side top the standings with a superior net run-rate to the Chennai Super Kings and the Rajasthan Royals, both of whom also have 20 points.