Australia's Travis Head made a 24-ball 62 to lead the assault after Hyderabad batted first and went past the previous IPL best of 263-5 by Royal Challengers Bengaluru in 2013.
Mumbai replied strongly in the match which witnessed 38 sixes for another IPL record, bettering the 33 hits over the fence clubbed three times in earlier seasons. Left-handed Tilak Varma stood out with his 64 in 34 balls for Mumbai but the effort was not enough on a batting-friendly pitch in veteran batsman Rohit Sharma's 200th IPL match.
Rohit smashed a 12-ball 26 and fellow opener Ishan Kishan made 34 to give Mumbai a flying start, but the innings lost momentum after 10 overs due to the ever-increasing asking rate.
Tim David smashed an unbeaten 42 in a late charge but the chase was beyond reach as Mumbai ended on 246-5 - the team's highest IPL total.
It was records galore as the match also featured the highest run aggregate of 523 runs in 17 years of the IPL.
Hyderabad skipper Pat Cummins was the best of the bowlers with 2-35 in his four overs of pace, leading his side to their first win of the season. Earlier the left-handed Head, dropped on five by David off skipper Hardik Pandya, reached his fifty in 18 balls and after his departure, Abhishek Sharma reached his half-century off just 16.
The team's 100 came up in only seven overs and Hyderabad posted the tournament's highest ever total in the first 10 overs of 148-2. Abhishek fell for 63 off 23 balls but there was no respite for the bowlers who were at the receiving end of some punishing batting.
It was raining boundaries in Hyderabad's innings with 18 sixes and 19 fours as the South African pair of Heinrich Klaasen (80 not out in 34 balls) and Aiden Markram, who hit 42, posted an unbeaten stand of 116.
Mumbai's South African import Kwena Maphaka had a bruising introduction to IPL when the 17-year-old left-arm quick went for 66 runs in his four overs.
Five-time winners Mumbai, who had a change in captaincy after Pandya took over from the experienced Rohit, and Hyderabad started this edition with a loss each.
