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 at Uppal.
With today`s 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 though did not have a good start in their run chase as they lost opener Chidhambaram Gautam (1) in the second over off pacer Bhuvneshwar Kumar but Simmons and Rayudu steadied the innings and then set up an easy win for MI.
They batted slow 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 in IPL-7.
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 as they hit occasional boundaries to keep the asking rate under control while also preserving wickets.
From 32 for one at the end of the fifth over, Mumbai reached 32 for one at the halfway stage and then 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, however, 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.
Rohit hit the winning runs — a four — as Mumbai reached 160 for three in 18.2 overs to notch up a much-needed win to stay afloat in the tournament.
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 electing 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 to take them to a fighting total.
Finch played the role of sheet-anchor as he stayed till the penultimate over of Hyderabad innings, sharing 63 runs for the third wicket with Warner from nine overs. He hit seven boundaries and two sixes in his 62-ball knock.
The in-form Warner was largely instrumental in taking the score past 150 as he smashed two sixes off Lasith Malinga in the penultimate over and two boundaries off the final two balls of the innings bowled by Kieron Pollar as Hyderabad scored 15 and 18 runs of the last two overs.
Warner`s 31-ball unbeaten knock was studded with six boundaries and two sixes.
Opener and captain Shikhar continued his struggle and he could contribute just 11 from as many balls in his side`s first match at home this season. He was out in the last ball of the fifth over with Malinga uprooting his middle stump as he went for a drive outside the line.
One-down Lokesh Rahul was run out in the 10th over while going for a non-existent single. He made frantic return to the crease after running half-way down the pitch, but not before Chidhambaram Gautam broke the stumps.
For Mumbai, Malinga took two wickets for 35 runs off his four overs.