The win was Chennai's third on the trot while Mumbai is yet to open their account in the tournament after having slumped to their third straight defeat.
Asked to bowl, Mohit (4/14) produced a fine death bowling display to help Chennai restrict the title holders to a modest 141 for seven.
Coming on to bowl the 19th over, Mohit picked up three wickets - Ambati Raydu, dangerman Kieron Pollard (12) and Harbhajan Singh - to prevent a late burst from Mumbai batsmen.
Mumbai's innings mainly revolved around captain Rohit Sharma and Correy Anderson. While Rohit made 50 off 41 balls with the help of three fours and two sixes, big-hitting Anderson scored 39 off 31 balls.
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In fact, the 84-run third wicket partnership between the duo was the highlight of Mumbai's innings especially after they lost their openers for just 25 runs inside five overs.
But once the duo departed their innings fell apart as Mumbai could manage just 33 runs off the last five overs for the loss of five wickets.
After two quiet overs, Smith took Pragyan Ojha to the cleaners and clobbered the left-arm spinner for two sixes straight over his head to get Chennai going.
Smith then slammed Zaheer Khan for another six before Brendon McCullum joined the party and struck consecutive fours to pick up 16 runs off the fourth over.
McCullum matched his partner stroke for stroke and welcomed Anderson with three cracking boundaries as Chennai raced off to 51 in just the sixth over.