The 29-year old Simmons provided the ideal start to the defending champions along with Michael Hussey when they were put into bat by Mahendra Singh Dhoni after winning the toss.
The duo piled on quick 76 runs in 58 balls before left-arm spinner Ravindra Jadeja shattered Hussey's stumps.
The pair attacked Mohit Sharma in the sixth over, milking him for 19 runs, with the West Indian Simmons scoring the bulk -- a four on extra cover, a six at mid-wicket and a four over point in consecutive balls.
New Zealand all rounder Corey Anderson, who came one-down, couldn't do much damage but his cameo of 20 runs off just eight deliveries consisted of a four and two sixes.
Simmons, who has been in good form throughout the tournament hit the bowlers all around the park and his 71 minutes stay at the crease yielded five fours and four sixes.
The Trinidadian, the only player to have scored a century this season, looked set for another big score but perished in the 17th over while trying to hit a big shot and was caught at long on by Suresh Raina off Jadeja.
Burly West Indian Kieron Pollard chanced his arm to hit a four and a six in his 14 but his departure triggered a batting order collapse as Mumbai started losing wickets in a clutch while trying to pace their innings.
Mumbai lost Pollard, Aditya Tare (0), Ambati Rayudu (2), Praveen Kumar (1) in quick succession to find themselves reduced to 166 for eight after the Simmons' departure at 163.
Mohit Sharma was expensive as he gave away 42 runs in his four overs but the Haryana pacer picked up three wickets, after conceding 25 runs in his first two overs. Ashish Nehra and Jadeja picked up two wickets a piece.
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