With Gold Coast toppling the Warriors earlier on Thursday, the loss saw Souths tumble back to the bottom of the NRL ladder.
Xavier Coates left AAMI Park in the 34th minute with hamstring tightness, but combined with five-eighth Munster for three first-half tries for a match-winning 32-4 halftime lead.
Souths scored three tries in nine minutes in the second half to briefly make is a contest, but it was too little too late.
Congratulations to Cameron Munster who was awarded the Spirit of Anzac Medal for player of the game! � — NRL (@NRL) pic.twitter.com/xmmCA2TvDMApril 25, 2024
Munster missed the first four rounds with a groin issue but was back to his  bamboozling best, using both his pinpoint kicking and passing game to set up the tries.Â
He then crossed for one of his own in the 66th minute to snuff out Souths' late challenge.
"It's very disappointing, especially with the two weeks lead-in that we've had and the detail in how we wanted to play, especially defensively," said Demetriou, with his side still only on one win for the season.
"It's just a myriad of errors defensively ...around our ruck, around our decision on our edges, we're just not nailing them when the pressure is on.
The Storm's Xavier Coates scores a try in his side's Anzac Day win over South Sydney. (Scott Barbour/AAP PHOTOS)
"You see periods where the team looks like the team we're capable of being but we need to buy in to doing it for longer periods."Â
Winger Taane Milne was sin-binned in the final minute and put on report for attacking Munster's legs, which Demetriou described as a "dumb note to end a dumb night".
Despite sitting second on the ladder heading into the match, Melbourne had only led once at the 70-minute mark in five wins, relying on some late heroics.
They had no such need against their new Anzac Day opponents, with the Rabbitohs replacing the Warriors in the annual fixture.
Souths were in the match until the 27th minute, only trailing 10-4, but the Storm piled on a further five tries before the halftime hooter and it was effectively game over.
The misery continued when fullback Ryan Papenhuyzen scooted over from dummy-half four minutes into the second half for his second try, but then the visitors were finally able to stem the flow.
Five-eighth Cody Walker and Jacob Gagai repeated a first-half effort, with the winger diving over for his second try.
Souths took advantage of Tyran Wishart covering Coates on the wing, with Milne brushing him aside to score in the 57th minute, before skipper Cameron Murray crossed two minutes later to close the gap to 36-20.
But Munster's try turned the tide back Melbourne's way, with Wishart and Joe Chan bringing the tally to 10 tries to stretch the Rabbitohs' record south of the border to 19 successive losses.
Storm coach Craig Bellamy said it was his spine's best performance of the season.
"We played really well the first half and I thought we defended well," he said.
"The first 20 minutes of the second half we probably took our foot off a little bit but I thought we finished really strongly - there was plenty of energy and plenty of intent so I'm really happy."
He said that while he didn't think Coates' injury was serious, he and also prop Nelson Asofa-Solmona (hamstring) could miss next round's clash with the Titans.
