Leading 20-18 with seconds to go on Saturday night, the Sharks let another win slip when Melbourne put the ball through eight sets of hands before a magical Harry Grant flick pass put Trent Loiero over.
This result alone is of little concern to the Sharks, given Nicho Hynes and Blayke Brailey were among four players rested with five-eighth Braydon Trindall also injured.
Coach Craig Fitzgibbon made his frustrations clear following fulltime around the referees, unhappy with decisions to award Melbourne's first two tries.
But he was insistent Saturday could be a turning point, after defeats to St George Illawarra, Canberra and Parramatta in the past month.
"We've been a bit out of sorts, a bit uptight. But you saw what we're about" Fitzgibbon said.
"That was awesome. We did everything we could to win the game.
"The only thing that is telling us the lie is the scoreboard."
Headed into Saturday night Cronulla simply needed to avoid a 50-point defeat to ensure fifth spot on the ladder, and an elimination final with the out-of-sorts Cowboys.
That briefly looked under threat when Melbourne led 12-0 early after two Sharks were sin-binned, before three Cronulla tries in an eight-minute period before halftime swung the game.
Storm No.7 Jahrome Hughes failed to finish the first half after another hamstring setback, in a concern for New Zealand's World Cup hopes.Â
Cronulla prop Addin Fonua-Blake ended the night on report for a hip-drop tackle on Cooper Clarke and faces a nervous wait to see if he can play next week.
Where that match will be played is now the biggest talking point.
Sharks officials will talk with the NRL on Sunday to learn if they will be able to play at home or be forced to go to Allianz Stadium.
Had Cronulla been handily beaten and slipped to sixth, they would have faced Newcastle and no chance of a Shark Park match.
But the Sharks will argue hosting the Cowboys would unlikely attract many more at Allianz than the 15,000 legally allowed at their traditional home.
The ferocity of the Shark Park crowd was on display in a dramatic start on Saturday night, when debutant winger Michael Gabrael was sin-binned for a high shot on Siulagi Tuimalatu-Brown.
The Melbourne winger was stretchered off and taken to hospital as a precaution, but the 22-year-old was conscious after suffering a concussion.
Ronaldo Mulitalo joined Gabrael in the bin moments later when he ran across the field and landed an open-handed slap on Grant, after Melbourne's captain hit Riley Pollard after kicking.
Cronulla fans were then fuming that a Nick Meaney pass wasn't called forward as he sent Hugo Peel over against an 11-man defence.
That anger intensified when Sua Fa'alogo was ruled to have got a ball down within millimetres of the dead-ball line, after chasing down a Grant kick.
But the mood turned before the break, when Pollard offered a glimpse of the future by helping lay on tries to Sione Katoa and rookie Riley Jones.
Siosifa Talakai also helped put Billy Burns over to give Cronulla the lead, before Melbourne's late heroics stole the show.
"It's been a tough season, and strange knowing we're not going to be in the finals," coach Craig Bellamy said.
"But I'm really happy with the way the boys went about it. We kept training well and competing.
"It was a close shave tonight ... But I am real proud of the way they finished."
Cronulla hope Trindall will come back from a shoulder dislocation at No.6, while prop Tom Hazleton can return from suspension.
South Sydney will host Newcastle in the other elimination final.
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