Mumbai leaked 41 runs in the last two overs bowled by Mitchel McClenaghan and Jasprit Bumrah, who went for 26 and 15 respectively.
Put in to bat, Pune found themselves under severe pressure after losing opener Rahul Tripathi and captain Steven Smith inside the first two overs.
A sharp and full inswinger from McClenaghan ripped through Tripathi's defense while Smith played a loose shot off Lasith Malinga, a mistimed flick that went really high before the ball settled in the safe hands of Hardik Pandya.
Rahane and Tiwary were now in the middle to resurrect the innings.
Rahane, who did not score big in the league stage, was determined to make an impact on the big stage.
A couple of boundaries off McClenaghan got him going, the second being a delightful cover drive.
Both Rahane and Tiwary kept the scoreboard ticking but were unable to clear the fence regularly.
Rahane eventually completed his fifty off 39 balls while Tiwary was on 30 off 29 balls when Pune reached 83 for two in 12 overs. To make the situation tougher for Mumbai, Rahane was adjudged leg before off Karn Sharma in the following over.
The visitors now needed the big hits badly to post a fighting total.
Dhoni walked in to join Tiwary and did not take long to hit his first six, depositing a half-volley off Karn Sharma over deep midwicket.
Karn, who was picked ahead of Harbhajan Singh for the crucial game, ended up with decent figures of 4 for 30 in four overs.
Tiwary too gave him good support during their 73-run stand off 44 balls, scoring four boundaries and two sixes in total.
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