In a dramatic start to this year's final series, the Rabbitohs appeared to have clinched a preliminary final when Cameron Murray controversially stormed over with nine minutes to go.
But Munster set up a line break for Billy Slater and then stepped up to nail a 31-metre field goal to send a raucous crowd of 17,306 at AAMI Park into raptures.
The Rabbitohs now wait on the winner of Sunday's elimination final between Brisbane and St George Illawarra to keep their season alive next week.
The Storm had to come from behind five times in an absorbing contest, and also had to overcome a number of controversial refereeing decisions, to claim the win.
Scores were locked at 18-all midway through the second half when Curtis Scott was penalised for a second effort in a tackle that led to Robert Jennings crossing not long after.
A Cheyse Blair try levelled the game again, only for a sideline official to rule a Josh Addo-Carr forward pass that led to Murray's go-ahead four-pointer.
But Munster's late game heroics ensured the Storm remain on track to become the first team to defend their crowd in a unified competition since Brisbane in 1992-93.
Blair and Suliasi Vunivalu both finished with doubles, while Rabbitohs skipper Greg Inglis did his best to inspire his side to also nab a double.
It was an explosive start to the qualifying final, with the hosts forcing an error in their first defensive set that almost ended in an opening try for Slater.
But the retiring fullback grounded a grubber on the dead-ball line, to which the Rabbitohs responded through an aerial raid for Dane Gagai to post first points.
The ferocious collisions kept on coming with Sam Burgess jolting the ball free on an early play, while Inglis also had the wind knocked out of him by Vunivalu not long after.
Poor defensive reads by the Rabbitohs, sandwiched by a stadium-shaking Kaufusi shot on Sam Burgess, ended in back-to-back Storm tries to Scott and Vunivalu and their first lead.
The visitors regained the lead on a bizarre 37th-minute Inglis try, where Vunivalu gave up on the play as he appealed for an offload from the ground from Jennings.
But Storm halfback Brodie Croft - a last-minute inclusion for Jahrome Hughes - broke the game open with a 70-metre line-break and grubber for Vunivalu on the stroke of halftime.
And it appeared the Storm were on their way when George Burgess was sin-binned for a professional foul that resulted in Cameron Smith kicking the Storm to a six-point lead.
However the Rabbitohs rebounded with back-to-back tries, only for the Storm to once again prove their big-game quality with another strong finish.
Rabbitohs halfback Adam Reynolds came off with a shoulder injury moments before the break but took the field upon resumption with what was described as a shoulder sprain.