Again it was errors - both in attack and defence - that cruelled many of their chances.
Trailing 24-10 midway through the second half, the Storm finally found some spark to score two quick tries to get back to within two points with nine minutes remaining.
It looked like they would fall short, but instead, St George Illawarra remain winless in Melbourne since 1999.
The game marked the return of former Storm five-eighth Gareth Widdop and while he impressed, the backs outside him starred.
NSW State of Origin fullback Josh Dugan, who is on the comeback from a knee injury, had a mixed bag.
The Storm targetted him with their kicking game and in the first half the pressure reaped rewards.
He let the home side score their second try when he slid under a Billy Slater kick, allowing Will Chambers to snatch the ball for the easiest of tries.
That gave Melbourne a 10-4 lead but the match was tied up when Slater himself spilt a bomb that allowed the Dragons to send the ball wide for winger Brett Morris to touch down.
Chambers then gave the Dragons a chance for the halftime lead when he was put on report for a shoulder charge that flattened Dugan, with Widdop on target with the penalty kick.
St George Illawarra came out firing in the second half and after a break by Dugan, Gerard Beale and Morris again combined with Beale taking the points this time.
Soon after the lead was out to 14 points after Storm winger Sisa Waqa dropped a kick cold that was pounced on by Trent Merrin for another try.
It looked like the Dragons would romp home but two Storm tries, scored by Chambers and Cronk in three minutes, gave them the chance to set up the heart-stopping finish.
"The footy gods weren't on our side" was how St George Illawarra coach Steve Price summed up his team's shock loss to Melbourne.
The Dragons were primed to snap a two-game losing streak and break through for their first win in Melbourne since 1999.
But a frantic try scored by Storm winger Young Tonumaipea after full-time gave the home team a thrilling 28-24 win.
The Dragons repelled wave after wave of Storm attack and it looked like they would hold on for the deserved victory.
It wasn't to be.
"It's totally gut-wrenching," said Price, whose team has now suffered three straight defeats.
"We were really courageous, the footy gods weren't on our side.
"It's tough to take."
The visitors finished down a man with Joel Thompson off with concussion.
Centre Dylan Farrell, who scored the opening try, was a first half casualty and will go for scans on a suspected torn pec.
Tonumaipea's try came after the Storm threw the ball wildly around the field after the final hooter before Ryan Hoffman found his winger.
The once impenetrable Melbourne fortress looked decidedly shaky until that final try, after falling to Gold Coast last round.
Again it was errors, both in attack and defence, that cruelled many of their chances until the final 20 minutes.
Trailing 24-10 the Storm finally found some spark to score two quick tries to get back to a two-point margin with nine minutes remaining.
The game marked the return of former Storm five-eighth Gareth Widdop and while he impressed, the backs outside him starred.
NSW State of Origin fullback Josh Dugan, who is on the comeback from a knee injury, had a mixed bag.
The Storm targetted him with their kicking game and in the first half the pressure reaped rewards with some notable errors.
He let the home side score their second try when he slid under a Billy Slater kick, allowing Will Chambers to snatch the ball for the easiest of tries.
Chambers then gave the Dragons the halftime lead when he was put on report for a shoulder charge that flattened Dugan, with Widdop on target with the penalty kick.
But in the second half a Dugan break led to a try by Gerard Beale, with Trent Merrin then taking advantage of a Sisa Waqa dropped ball to blow the lead out to 14 points.
Storm coach Craig Bellamy said he felt it "surreal" that he side trailed by so much.
"I just thought we played really well the last 20 minutes and I was really happy with that," he said.
"To win like that, we obviously had a little bit of luck there but at a couple of other stages luck probably deserted us so it was nice to get that at the end."
- AAP
