The hosts set a new IPL record of 3 for 277, but Mumbai put up a fierce fight in their chase before ending up 31 runs short on 5 for 246.
It was little consolation but they contributed to a new record aggregate of 523 runs, surpassing the 517 set by South Africa and the West Indies a year and a day ago.
The match finished with 38 sixes, another record for the most hit in a T20 game.
Aussie opener Travis Head gave Sunrisers an explosive start with 62 from 24 balls and Abhishek Sharma contributed 63 off 23, but  South Africa's Heinrich Klaasen was the star turn, smashing 80 not out off 34, including seven sixes and four fours.
Aiden Markram made an unbeaten 42, with a strike rate of 150, as Sunrisers surpassed the previous IPL best of 5 for 263, set by Royal Challengers Bangalore against Pune Warriors in 2013.
Mumbai set off at a tremendous pace, thrashing 56 runs off the first 19 balls.
They kept pace for a long time - reaching 150 in the 10th over - but all five batters were caught as they tried in vain to match the huge asking rate.
Hyderabad captain Pat Cummins, right, and Shahbaz Ahmed celebrate the dismissal of Ishan Kishan. (AP PHOTO)
Pat Cummins, the Sunrisers captain, took the key wicket of opener Rohit Sharma (26 off 12 balls) and later Tilak Varma (64 off 34).
Varma's wicket effectively ended the chase as it left Mumbai 4 for 182 in the 15th over.
with agencies
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