Smith steered his side's chase with a 63-run unbeaten knock that came of just 47 balls with the help of four boundaries and three sixes as Mumbai overwhelmed the 140-run target in 18.3 overs overs.
Kieron Pollard also played an unbeaten 32-run cameo towards the end which was studded with two fours and three huge sixes sixes to help Mumbai's cause.
Earlier, Mumbai produced a fine bowling display to restrict the Lions to a modest 140 for five.
Opting to bowl, Mumbai pacers utilised the seaming conditions of the Sawai Man Singh Stadium pitch before their spinners came to the party to stop Lions from posting a formidable total.
Mumbai will next play Perth Scorchers in Delhi on October 2, while the Lions will take on Otago Volts in their next game here on Sunday.
Chasing the target, Mumbai suffered a big blow early losing the wicket of Sachin Tendulkar (5) in the third over. Tendulkar was undone by a slower delivery from Sohail Tanvir as the ball went through his defence to crash onto the stumps.
Smith and Dinesh Karthik added 31 runs for the second wicket before the latter cut leg-spinner Imran Tahir straight to Petersen at backward point as Mumbai slumped to 47 for 2.
Smith, however, continued his attacking game and together with captain Rohit Sharma (20) kept Mumbai in the hunt, sharing 43 runs for the third wicket in just five overs.
Smith was at his aggressive best as found boundaries with ease to notch up his fifty in just 33 balls. Rohit provided him able support from the other end before perishing in the 13th over, caught by substitute fielder Bavuma off Dwaine Pretorious. He struck two fours during his 17-ball knock.