The decision to bat seemed to have backfired as Mumbai managed only 45 runs in the first 10 overs but the fiery 104-run stand between Pollard and Anderson in just 9.1 overs, changed the team's fortunes.
Pollard's 70 came off just 34 balls as he punished the Royals bowlers with seven fours and five sixes while Anderson supported the Caribbean with a 38-ball 50.
The Royals bowlers, who had straight-jacketed the Mumbai batsmen for the major part of the innings, were clueless against the Caribbean stroke-maker and Anderson, who got life on 23 after being caught off a no ball.
Not only this, Mumbai opener Aaron Finch pulled a hamstring while attempting a single in the fourth over, bowled by Stuart Binny. Helped by teammates, Finch (10) limped back to the dugout, unable to keep his left leg on the ground.
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Unmukt Chand joined Parthiv Patel at the crease but the left-hander offered a simple catch to Chris Morris off Dhawal Kulkarni to be dismissed for 16.
Kiwi paceman Tim Southee was very effective with his outswingers while Kulkarni also kept a very tight line. Binny too bowled a probing line and was rewarded soon as he scalped rival captain Rohit Sharma (0), who edged one to slips.
Such was the discipline and domination of the Royals' bowlers that Mumbai scored only 45 runs in 10 overs, managing only six shots to the fence.
Pollard broke the shackles by dispatching a Chris Morris delivery to boundary ropes and then Anderson lofted the same bowler two balls later for another four. The Caribbean smashed James Faulkner for a six over mid-wicket.
Anderson was caught off a no ball from Kulkarni and he made the Royals pay for that mistake immediately, hitting Southee for a massive six and followed it up with a four.