According to BBC Opener Travis Head hit 62 from 24 balls, Abhishek Sharma a 23-ball 63 and Heinrich Klaasen 80 not out from 34.
They took Sunrisers beyond the previous IPL record, Royal Challengers Bangalore’s 263-5 in 2013.
Mumbai made a decent fist of the chase, making the match the highest-scoring T20 in history, but ended on 246-5.
Sunrisers’ total was also the fourth highest in any men’s T20 and the highest in a T20 franchise tournament.