Gold Coast winger Anthony Don scored with two minutes remaining in the match, with Aidan Sezer's conversion hitting the uprights but bouncing through to tie up the score and send the match into extra time.
Cronk missed three field goal attempts in golden point before a long-range attempt scraped over with two minutes remaining.
The shattered Titans needed to win and hope other results fell their way to book a place in the NRL finals.
Melbourne are set to play the minor premiers Sydney Roosters in a qualifying final next Saturday night at Allianz Stadium unless Penrith upset Manly in their final round clash.
It was a heart-stopping finale at AAMI Park.
Gold Coast looked to have scored six minutes before Don's try when Sezer scooped up a loose Billy Slater pass and touched down under the posts.
However video referees Chris Ward and Justin Morgan ruled that Ben Ridge had hit the ball from Slater's hands which meant a knock-on and no try.
But the Titans refused to give up, throwing everything at the champions.
The under-strength visitors led 16-12 at halftime, with a rampaging Dave Taylor scoring one try and setting up another in his best performance of the season.
Titans co-captain Nate Myles was a late withdrawal due to an ankle injury, with Taylor elevated from the bench into the starting side.
The giant forward proved unstoppable at times in the first half.
But the Storm upped the tempo in the second half and starved the Titans of possession.
They levelled with a try through winger Sisa Waqa and then centre Will Chambers ran on to a Slater ball to give his side the lead in the 56th minute.
Slater himself finished with two tries.
While Melbourne got the win, it wasn't the performance coach Craig Bellamy wanted after their 28-8 loss to Manly last round.
They also lost five-eighth Brett Finch to a sternum injury late in the first half with the possible return of England international Gareth Widdop timely.
Widdop is playing in the Queensland Cup on Sunday in his comeback from a dislocated hip.
MELBOURNE 23 (B Slater 2 W Chambers S Waqa tries C Smith 3 goals C Cronk field goal) bt GOLD COAST 22 (A Don B Takairangi D Taylor tries A Sezer 5 goals) in golden-point extra time.
Referees: Shayne Hayne, Gavin Morris.
Crowd: 13,826 at AAMI Park.