Mohsin, an up-and-coming left-arm quick who returned figures of 1-26, defended 11 off the final over as Mumbai fell short of their 178-run victory target in Lucknow.
Tim David gave Lucknow a scare with his unbeaten 19-ball 32 but he and fellow Australian Cameron Green could do little against Mohsin's yorkers and discipline at the death.
Impact player Yash Thakur and leg-spinner Ravi Bishnoi took two wickets each to add to Lucknow's bowling attack.
Lucknow swapped places with five-time winners Mumbai to jump to third in their bid for a top-four finish in the group stage for a play-off berth.
"We just lost the game. We didn't play well enough to win," said Mumbai skipper Rohit Sharma. "There were moments we didn't win. Unfortunate but we need to keep our heads high."
Holders Gujarat Titans have already booked their spot and assured a top-two finish. Seven off the 10 teams are fighting for the three remaining play-off places.
Stoinis set up victory for Lucknow after he put on key partnerships including an 89-run stand with skipper Krunal Pandya, who retired hurt on 49, to guide Lucknow to 177-3.
The Australian all-rounder walked in at 35-3 and rebuild the Lucknow innings with the left-handed Pandya on a not-so-easy pitch to bat.
Pandya was cramping in his knock and retired one short of fifty but Stoinis soon changed gears as he raised his fifty with a six and lay into Chris Jordan in a 24-run 18th over.
He put on an unbeaten 60-run standoff 24 balls with Nicholas Pooran, who made eight, and finished the innings with a six.
"We have shown that we are a real team, there no superstars, there are different people performing for us," said man of the match Stoinis.
In reply, Ishan Kishan smashed 59 and put on a 90-run opening stand with Rohit, who made 37.
Bishnoi sent the two back in the pavilion and Thakur got the big wicket of Suryakumar Yadav, for seven. Mumbai soon slipped to 145-5 in 17.4 overs.
David attempted to pull the chase with Green for company but Mohsin and Lucknow held their nerve.
