Daredevils, believed to have the best bowling attack, restricted the hosts 142 for eight but were terrible in run chase, managing for 128 for seven in 20 overs.
Leg-spinner Amit Mishra returned exceptional figures 4-0-18-2 while Australian paceman Pat Cummins (2/20) also chipped in with two wickets in Daredevils' good bowling show.
It was a collective bowling effort from Daredevils with Kagiso Rabada (1/30), who made his IPL debut, and skipper Zaheer Khan also contributing in choking the Mumbai line-up which is full of devastating batsmen.
Daredevils were gasping at 24 for six inside the seventh over after McClenaghan (3/24) took three wickets.
A 91-run partnership between South Africans Kagiso Rabada (44) and Chris Morris (52) raised their hopes but it only reduced the defeat margin.
Mumbai Indians consolidated their position at the top with sixth win in a row.
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