Opener Simmons (68) and Rayudu (68) frustrated Hyderabad bowlers for 14.3 overs during which they shared 130 runs for the second wicket as Mumbai chased down the target of 158 with eight balls to spare at the Rajiv Gandhi International Cricket Stadium.
With the win, their third from nine matches, Mumbai jumped to sixth spot with six points while Hyderabad remained on fifth position with eight points from nine matches.
Mumbai did not have a good start in their chase as they lost opener C M?Gautam (1) in the second over off pacer Bhuvneshwar Kumar but Simmons and Rayudu steadied the innings and then set up an easy win.
They batted steadily for a while before Simmons took 16 runs off Irfan Pathan in the fifth over with two sixes and a four. Pathan was the unfortunate bowler as he was also picked by Rayudu for special treatment later on and the pacer conceded 29 runs from his two overs.
Leg-spinner Amit Mishra was also expensive as he conceded 33 runs from his three wicketless overs to add to the woes of Hyderabad who were playing their first match at home.
Rayudu, who hit seven fours and two sixes off 46 balls, and Simmons, whose 50-ball knock included five fours and four sixes, batted sensibly, keeping the asking rate under control while also preserving wickets.
From 32 for one at the end of the fifth over, Mumbai raced away to 125 for one at the end of the 15th over and the asking rate had been brought down below seven an over by then.
The duo were out in quick succession — in the 16th and 17th overs off Bhuvneshwar (2/21) and Moises Henriques (1/23) respectively — as Mumbai faced some jittery moments towards the end before skipper Rohit Sharma (14 not out) and Kieron Pollard (6 not out) took their side home.
Earlier, a late assault by David Warner (55 not out) after a solid batting show by opener Aaron Finch (68) took Hyderabad to 157 for three after they elected to bat. Hyderabad were tied down for most part of their innings and it seemed they would fall short of 150 before the last two overs yielded 33 runs.