Australian cricketer Smith, who replaced Ajinkya Rahane as the captain of Rajasthan franchise, played skipper's knock to achieve the target set by Rohit Sharma-led Mumbai.
Smith scored an unbeaten 59 off 48 and he was well supported by Riyan Parag (43) and Sanju Samson (35).
For his match-winning knock, Smith won Man of the Match award.
While reciving the award, he said, "I haven't contributed as much as I would've liked through the tournament and it feels really nice to have gotten the boys over the line."
"Hopefully we can carry it forward from here," he added.
Earlier, batting first, Mumbai put up a decent 161 for 5 against thanks to Quinton de Kock's splendid knock.
De Kock smashed 65 off 47 balls with six fours and two sixes, adding 97 runs off 68 balls for the second wicket with Suryakumar Yadav (34 off 33 balls) that helped MI total gain a semblance of respectability.
Reinstated as skipper in place of Ajinkya Rahane, Steve Smith introduced leg-spinner Shreyas Gopal (2/21 in 4 overs) in the third over.
He deceived rival skipper Rohit Sharma( 5), who stepped out only to offer a return catch after failing to read a googly.
Gopal could have got rid of De Kock off the last ball of the over but Jofra Archer dropped a difficult chance at long on.
Making most out of this reprieve De Kock helped his team reach 50-run mark in 6.5 overs.
He reached his own half-century in 34 balls and his partnership with Suryakumar was broken when latter was caught in deep off Stuart Binny in the 14th over.
A few balls later Quinton de Kock too was holed out in long-on as Hardik Pandya and Pollard joined forces with scorboard reading 112 for 3 in 15 overs.
Pollard(10 runs 7 balls) was dropped by Archer once again. Hardik played another of his cameos scoring 23 off 15 balls.
Smith, who replaced Ajinkya Rahane as the captain of Rajasthan franchise, played skipper's knock to achieve the target set by Rohit Sharma-led Mumbai