The victory was their second after a five-game losing streak but the Storm looked far from the pace-setting side that rolled through the start of the season with nine successive victories.
The Titans set up a heart-stopping finish when they scored a converted try with 10 minutes left after David Mead pounced on a pin-point kick by five-eighth Aidan Sezer to close the gap to 18-16.
But the home side sealed the result as the ball went through six pairs of hands on the final tackle before finding try-scorer Gareth Widdop.
Melbourne trailed 10-0 at halftime but responded to a massive blast from coach Craig Bellamy in emphatic style, scoring two tries through Billy Slater and Cooper Cronk in the opening six minutes of the second half to lead 12-10.
The ninth-placed Titans, desperate for some NRL finals action, didn't lie down but, when Storm lock Ryan Hoffman slid across for a try in the greasy conditions for an eight-point lead, it was an uphill battle for the visitors.
Compounding the task for Gold Coast was losing prop Luke Bailey to an Achilles injury in only the eighth minute and then lock Ashley Harrison midway through the half with a glute injury.
Melbourne took advantage of their opponents' two-man bench to make inroads up the centre of the field which was something they failed to do in a disappointing first half.
Mahe Fonua became the first Victorian player to make his first grade debut when he was called in for winger Anthony Quinn but he had a nightmare opening 20 minutes.
The 19-year-old dropped the ball with his first touch three minutes into the game, was caught out of position which handed the Titans their first try to centre Steve Michaels, and then spilled a simple Slater pass.
The youngster found his feet and was unlucky not to finish with a try.
Storm coach Bellamy said he "lost his cool" after a disappointing opening 40 minutes, surprised his team had started so badly after their promising effort last week.
"The Gold Coast were out-muscling us, out-working us, they were out-enthusing us," Bellamy said.
"I was really disappointed in that first half.
"I'm not quite sure what happened after last week - whether we got comfortable.
"You'd hate to think that after five losses."
He said his side wouldn't go far into the finals if they didn't improve.
Gold Coast coach John Cartwright said Bailey's season was over, although the severity of his Achilles injury wasn't clear.
Harrison will also have a scan on Monday while Greg Bird suffered rib cartilage damage and could miss their next clash against Parramatta on Sunday week.
Cartwright said the opening 10 minutes of the second half, when the Storm scored twice, was the worst possible scenario when they were down on troops.
"It was the worst thing that could have happened with what we had available to us, it was our worst nightmare.
"It was very hard to recover once they had a sniff."