In his 45-ball 51-run knock, Rohit struck two sixes and four boundaries to help his team to a modest total after it struggled to force the pace for a major part of the innings at the Barabati Stadium.
Sunil Narine bowled a very economical final over, conceding just four runs besides dismissing Rohit.
Struggling against the pace of Morkel, Gautam charged down the track against the lanky pacer but failed to clear cover where Suryakumar Yadav took a good catch.
Coming in for Jacques Kallis to strengthened the spin department, Shakib bowled an arm-ball that kept low and disturbed Simmons' leg stump as the batsman went for a heave.
The wicket ensured the Bangladesh left-arm spinner made up for a drop catch in the previous over.
After reaching 33 off 27 balls, Rayudu holed out at long-on while trying to force the pace, the successful bowler being Piyush Chawla. He hit 3 fours and a six.
It could have become 70 for four but for Yusuf Pathan's failure to hold on to a sitter at long-on, giving Rohit a life and Morkel a reason to express anguish. To end the over, Rohit got a boundary off a top edge.
Corey Anderson broke the shackles with a six and a four off Chawla in the 14th over, the maximum going long and high over the sight screen. It was a productive over for MI as they picked 17 runs off it.
Sunil Narine came back to bowl a tight over and peg MI back once again. At the end of the 15th over, Mumbai were struggling to step on the gas at 99 for three.
But Rohit soon freed his arms to loft Morkel over long off for a six. Another length ball followed and Rohit effortlessly launched the 146-kmph delivery over extra cover.
Having taken a beating, Morkel had something to cheer about as he had Anderson caught at midwicket in what was a soft dismissal.