Dwayne Smith (47), Brendon McCullum (49) Suresh Raina (35*) and Aaron Finch (33*) batted ruthlessly to touch the 172 runs target by losing only three wickets.
Pune earlier posted 171 runs for the loss of eight wickets.
Finch smashed three boundaries and two sixes in his 19-ball knock to clinch the match.
Earlier, Pune 171 runs at the scorecard.
Steve Smith scored the highest run for the side with his 43.
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