MI kept picking wickets in the middle despite Virat Kohli's effort.
Royal Challengers have fared the worst among all teams at the death this tournament, giving up 12.49 runs an over.
After being put to bat first, Umesh Yadav ripped apart through the Mumbai Indians batting order. On Tuesday, he was rewarded with the brand new ball on a cloudy evening. On the last ball of the 18th over by Jasprit Bumrah, Yadav was caught by Rohit Sharma as he slogged the ball to cover.
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Should the pitch behave similarly, Mumbai might find it hard to stop the top four of Bangalore - Quinton De Kock, Brendon McCullum, Virat Kohli and AB De Villiers. He bowled his first two overs in the Powerplay and went for 16 and was then only brought on in the 19th over.
Mumbai's method was effective, but peculiar. He paired with Evin Lewis (65) for a 108-run stand, posting his own half-century from just 32 balls. The start from the openers was promising - they added 40 off the first overs - but Mitchell McClenaghan turned the game on its head in a single over. On Tuesday night, that would turn into three in four.
Both batsmen were cleaned up through the gate as they attempted booming drives through the off side, before Rohit successfully negotiated the hat-trick ball.
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Interestingly, in the last two seasons, Mumbai have beaten Bangalore on all four occasions. "We have got few days before we play the next match on the 22nd (April), we will assess (him) and hopefully he will be fine", Rohit said.
Royal Challengers were never in it in the chase.
After a quick start in de Kock's company, Kohli settled for drives down the ground, nudges for ones and twos - sometimes even off full-tosses - and shots dropped pitchside.
Lewis eventually perished, having crashed six fours and five sixes, but Rohit maintained the momentum and was joined by Hardik Pandya in the penultimate over. In 10 completed seasons of the IPL, teams have missed making the final four because of net run-rate as much as four times.
Mumbai's spinners found plenty of grip and looked altogether more menacing than Royal Challengers' duo.
Krunal Pandya and Kieron Pollard then fell relatively cheaply, but skipper Sharma continued to score freely. And after Mumbai picked the first five Bangalore wickets for less than 100, it was up to the Bangalore captain to keep the fight going.
"It wasn't the ideal situation and I thought Umesh bowled in the right areas", There's always something for the seamers in the first six overs, but the wicket was still soft when I came in, so just wanted to assess the situation and pace my innings", Mumbai Indians captain stressed.