With just two men on the bench after the opening 20 minutes and the Sharks' right edge decimated, Cronulla piled on the points before doing enough to hold on.
The win moved Cronulla into the NRL's top four, with the club also set to benefit from a State of Origin period where they are likely to lose no players at all.
One of the premiership favourites before the season, Cronulla looked a shadow of their best in the last game at Shark Park at the end of March.
But in the seven weeks since, Fitzgibbon's men have now won five games, with Saturday night's victory over Melbourne the best of the lot.
But it didn't come easy, after the Sharks lost the right-edge pairing of Jesse Ramien (eye) and Samuel Stonestreet in the first 21 minutes of the match.
A makeshift pairing of forward Siosifa Talakai and utility Daniel Atkinson stood up, combining for two tries and doing enough to repel the Storm's attack.
Cronulla prop Addin Fonua-Blake was also immense, scoring a try, running 229 metres and making 109 of them in post-contact.
Blayke Brailey is playing with purpose running out of dummy-half, while Will Kennedy had an off night under the high ball but still had a bat-on pass for a try.
Cronulla led 25-12 at halftime and 31-22 late, but did enough to deny two Storm comebacks despite a hat-trick from Melbourne flyer Xavier Coates.
Even the end was dramatic, with the game boiling over twice in the final 20 seconds and NSW Origin hopeful Ryan Papenhuyzen on report for a hit after the siren.
Fitzgibbon labelled the win one of the best since he began coaching at the club in 2022.
"There was a bit of turbulence through the game," Fitzgibbon said.
"Playing Melbourne, you're not going to get it all your own way.
"But what I loved about it, as Sharks we kept finding ways to pick each other up and keep going. So it was good."
For Melbourne, the story was not so bright.
They remain third on the ladder, but haven't strung two straight wins together since rounds five and six and now face a difficult Origin period.
Saturday night's first half marked their worst defensively in 22 years, with Talakai and Atkinson having a role to play in Cronulla's attack.
That was evident almost immediately, with Talakai firing a perfect flick pass out the back while in contact for Atkinson's first try on the wing.
The Storm repeatedly targeted the pair in defence, with Coates' second try coming when he got outside Atkinson and third a result of leaping high above the utility.
But ultimately it was the makeshift pairing that had the last laugh, with quick hands from Talakai putting Atkinson over for the only try of the second half.
"We've been a bit inconsistent and we just need to work out what's important to make sure we're more consistent with it," Bellamy said.
"It's concerning whether Origin is on or not.
"We need more consistency in our game, because in the time I've been at the Storm that's been one of our strengths.
"We haven't always been the best team, but we've been consistent with what we see is important in our footy."Â
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