The Sharks will go into a bye off the back of two losses after falling to the Storm 30-6 in a grinding match at AAMI Park on Sunday.
The contest was closer than the scoreline suggested, with Cronulla going into half-time down 10-6 and staying within a converted try until the 64th minute.
Melbourne second-rower Eli Katoa was the star, claiming the opening try in the fifth minute with a piercing run before setting up two of his team's second-half tries by skilfully reeling in bombs and offloading to an outside man.
Sharks five-eighth Braydon Trindall crossed for the visiting side's lone four-pointer in the shadows of half-time after cleaning up a Nicho Hynes kick.
Cronulla now sit in 10th position ahead of a break next weekend, however they're level with the eighth-placed Dolphins on 18 competition points leading into important clash with the Redcliffe-based side in Round 19.
It was a clinical start from the Storm, with a surgical Jahrome Hughes short ball putting Katoa into a hole. Ryan Papenhuyzen converted for an early 6-0 lead.
Melbourne continued to dominate possession, but Cronulla courageously withstood wave after wave with committed defence before launching a counterattack. A seven-tackle set turned the tide, but an error halted the visitors' momentum just as the Sharks had set up inside the Storm's red zone.
Still, with Melbourne having 61% of the ball through 22 minutes, the tight scoreline reflected a wholehearted approach from Cronulla against their fierce rivals.
The Sharks found success down their left edge, but twice Sua Fa'alogo intervened by knocking down centre Sifa Talakai's attempted passes to an unmarked Ronaldo Mulitalo. The Storm flyer came up trumps a third time with Cronulla pressing hard, intercepting a bat-on from Hynes and dashing 90 metres to score.
Five minutes from half-time, Hynes played a key role in getting the Sharks on the scoreboard. The halfback launched a towering bomb which Faalogo didn't contest, allowing Trindall to swoop on the scraps and touch down.
A Sharks error early in the second half, followed by a penalty, allowed Melbourne to extend their lead to a converted try via the boot of Papenhuyzen.
A high-quality arm-wrestle ensued when play restarted as the teams traded sets in willing fashion. The Storm looked set to go up 14-6 when Papenhuyzen approached another penalty goal in the 60th minute, but the No.1 pushed it wide.
The home side then squandered another attacking opportunity after Trindall was pinged for a late hit, coughing up the ball in try-scoring range.
It took a special effort from Katoa to engineer Melbourne's first try since the 26th minute. The edge forward flew high to snatch a pinpoint Hughes bomb from under the nose of Will Kennedy before popping a pass for centre Nick Meaney.
A golden chance to peg back the margin went begging for the Sharks when a Trindall kick fortuitously bounced into the crossbar and straight into the path of Talakai, who unfortunately slipped at the last moment and fumbled the Steeden.
Moments later down the other end, the Storm seemingly put the game to bed as Fa'alogo crossed in the corner. But the Bunker disallowed the try, ruling the flanker's leg hit the sideline chalk just before he grounded the ball.
It mattered little. In a carbon copy of the previous try, Katoa again soared above Kennedy to pluck a bomb, this time offloading for Hughes to score.
The Storm capped off the afternoon with a try to Trent Loiero in the 78th minute.
