Chasing Mumbai's 184 runs for the loss of eight wickets, Pune reached 187 runs by losing three wickets with Smith playing the most vital role in the innings.
Smith seven boundaries and three sixes as he remained unbeaten at 54-ball 84 to help his side win their first match in the cash-rich series.
MS Dhoni remained unbeaten at 12 at the end end of the crease.
Ajinkya Rahane earlier contributed 60 runs.
Mumbai Indians earlier posted 184 runs for the loss of eight wickets in their 20 overs.
Jos Buttler (38) smashed three boundaries and three sixes in his knock.
On the other hand, Hardik Pandya hit one boundary and four sixes in his knock to post 15-ball 35 runs.
For Rising, Imran Tahir picked up three wickets.
Bengal lad, Ashok Dinda gave away 57 runs in his four overs.
Image: IPL twitter page
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