Batting first, MI scored a stiff 178 for three riding on half-centuries from Lendl Simons (62) and Mike Hussey (56).
In reply, Royals were never in the chase as they were restricted for 153 for eight. Karun Nair with 48 off 24 balls was the lone ranger for the Royals. Brad Hodge (40) and James Faulkner (31) tried their bit but it was too late by then.
It was a collective effort by the MI bowlers led by senior pro Harbhajan Singh, who outshone others with brilliant figures of two for 13 from four overs. Pragyan Ojha also did his bit with two for 30 from his four overs.
Roayls with 14 points from 12 games remain third in the table and firmly in the hunt. But back to back losses will certainly affect their chances of finishing in the top two which would have given them an additional game.
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Mumbai now have eight points from 11 matches.
Unmukt Chand (2) finally got a game but could well be the last one in the tournament. It was a rank bad delivery from Pragyan Ojha and Unmukt failed in his bid to play a proper pull-shot as Mike Hussey made no mistake at the deep mid-wicket boundary.
Sanju Samson (2) also played early to a Krishmar Santokie slower as Rayudu got his second catch as Royals were reduced to 42 for three.
While Karun was playing his strokes at other end, Kevon Cooper was dismissed by a sheer piece of fielding brilliance from Kieron Pollard standing at the long-on boundary. Cooper hit a Harbhajan delivery which would have been a sure six had any other fielder save Pollard manning that area.