The Royal Pune Supergiant captain led by example with an unbeaten 84 off 54 balls, including two sixes in a row in the final over, to guide his side to a seven-wicket victory with one ball to spare at the Maharashtra Cricket Association Stadium on Thursday night.
RPS secured the services of Ben Stokes, who became the highest paid foreign player in the history of the tournament.
"Form is form anywhere, I guess, so you got to make the most of it when you're hitting the ball well", said Smith who had hit a magnificent hundred while leading Australia to a Test win here during the recent series.
For Rising, Imran Tahir picked up three wickets.
After Rahane departed, with Nitish Rana holding his nerves to take a splendid catch deep at square leg, Smith took charge to enable his team to post a solid win.
Earlier, Hardik Pandya's late heroics took Mumbai Indians to 184 for 8 after leg-spinner Imran Tahir produced a sensational three-wicket burst in the space of 10 balls.
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Smith then joined Rahane in the middle and the duo added 58 runs in the space of seven overs to lay the foundation of a successful run chase.
On a surface that played true to it itself for the first time in many IPL matches played here, Rahane straightaway got into the top gear to punish Hardik Pandya's medium pace for three boundaries in the second over.
Buttler took his attacking game to the next level as he punished, fellow Englishman and this IPL's costliest buy, Ben Stokes for consecutive sixes in his maiden IPL over as Mumbai Indians raced to 41 for no loss in four overs. Buttler, who had scored 38 runs off just 19 deliveries, looked very displeased with the decision and the replays showed that he had got a thick inside edge. Bhatia then cut short Krunal Pandya's (3) stay at the crease to just five balls to reduce Mumbai to 107 for five in the 14th over.
Earlier in the day, a quickfire knock by Jos Buttler followed by a 30 run last over off Ashok Dinda's bowling led to Mumbai reaching a highly respectable total of 184 in their 20 overs.
His only wicket during that spell was that of West Indies all-rounder Kieron Pollard.