They succumbed to their third defeat of the season against their Maharashtra rivals in the first qualifier at Wankhede Stadium on Tuesday.
Powered by Mahendra Singh Dhoni and Manoj Tiwary, Pune scored 41 off their last two overs to finish at 162/4. To make the situation tougher for Mumbai, Rahane was adjudged leg before off Karn Sharma in the following over.
Mumbai, a two-time champion, has one more chance to make the final, when it plays the victor of Wednesday's (Thursday NZT) eliminator between defending champions Sunrisers Hyderabad and Kolkata Knight Riders on Friday.
On a wicket that was on the slower side, Mumbai were expected to chase down Pune's 162 easily but first they lost Lendl Simmons, who was run out, and then Rohit Sharma was wrongly adjudged LBW as replayed suggested their was an inside edge.
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Where Mumbai Indians drove the nail deep?
Pune lost two quick wickets - Rahul Tripathi was bowled in the first over and Lasith Malinga dismissed Steve Smith in the next -and their innings never really took off. Until the penultimate over.
Ajinkya Rahane and Major Tiwary steadied the early wobble with an 80-run stand, but struggled to keep the run rate up.
At one stage, Mumbai's Rohit Sharma almost ended up in Smith's lap while trying to catch one of Dhoni's sixes as it sailed over the boundary rope.
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Ambati Rayudu, who had replaced Nitish Rana in the previous game and played a gem of an innings against Kolkata, walked in at 4 but lasted just two balls after which he tried to pull a long hop from Sundar to the mid-wicket fence. Sundar had turned the match on its head with two wickets in an over conceding just a single run. Tiwary slammed a four off McClenaghan on the first ball, when the umpire signalled no-ball. Tiwary, who stayed with the former Indian captain to the end chipped in with a important 58 of 48 balls. The over produced 26.
In the 20th over, Tiwary made a decision to take a single and watch the show as Dhoni first went over covers off Jasprit Bumrah and then went for a double off a mistimed pull.
Dhoni sizzled in the final stages, scoring a scorching 40 of 26 balls.
On the other hand, Pune will desperately miss the services of their costliest buy this season, England's Ben Stokes, who will join his national side ahead of the International Cricket Council (ICC) Champions Trophy, next month.
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Meanwhile, a security researcher in the United Kingdom discovered a "kill switch" in WannaCry, further mitigating its impact. It wasn't immediately clear to what degree nations across Asia were being affected by the attack Monday.
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