With halfback Luke Brooks a late withdrawal with a shoulder injury, the Tigers had been strong through the first 10 minutes but Melbourne dominated much of the first half from then on.
Cronk put Will Chambers in the clear in the 36th minute and the Queensland winger easily beat a slipping fullback Mitchell Moses to score a 35m try for Melbourne to go to the break 18-6 ahead.
Cronk then kicked for a flying Sisa Waqa on the opposite wing to Koroibete 10 minutes after the break and the Maroons playmaker then combined with his fellow Queensland stars Billy Slater and Cameron Smith when the No.9 scored in the 54th minute.
Those were the last points of the match as emotions almost boiled over for the frustrated Tigers in the final 20 minutes, with a number of heated incidents between the two sides.
Tigers winger Pat Richards left the field with a hamstring injury in the first half and didn't return to add to a mounting injury toll.
Akauola was placed on report for a shoulder charge on Slater late in the second stanza.
Internal rumblings over the future of coach Mick Potter appear to have taken their toll on the 12th-placed Tigers, who have lost four of their last five matches and realistically need to win four of their five remaining games to make the finals.
Storm coach Craig Bellamy was pleased to get away from Campbelltown with two points.
"We have only played here a couple of times here before so it was a good result for us," he said.
"It is a tough place to play.
"I thought the boys played really well tonight, the Tigers were really up for it and put some pressure on us early.
"We weathered the storm so to speak and got into the rhythm of our game.
"That's what we wanted to do."
Tigers coach Mick Potter said his team struggled to keep up their early intensity.
"They came up with some good plays and they burnt us," Potter said.
"We just didn't quite have the same polish on our play.
"I thought they defended really well and put some pressure on us.
"They got the better of us."
Potter said he doubted both Brooks and Richards would be fit for Saturday's clash with North Queensland in Townsville.
"We just need to try and scrounge a win and do it quickly," he said.
- AAP