Friday's result, sealed by a second-half double from winger Jethro Rinakama, snapped a six-game losing run for the Bulldogs whose performances - both with and without the ball - have been heavily criticised.
Despite a nervy first opening 15 minutes at Accor Stadium, where Storm winger Moses Leo scored two tries in quick succession, the ferocious defensive traits of Canterbury's 2025 season looked to have returned.
Ciraldo paid tribute to his players for keeping on course despite their recent struggles.
The win over Melbourne leaves his side with four wins from 11 games ahead of a clash with Wests Tigers.
"As much as we say to try and block it out I think it's hard to ignore all of it, the outside noise, the rumours that circulate, and the bullshit that gets made up," Ciraldo said.
"I'm really proud of this group that they just kept turning up and trusting in what we were doing, but I felt a lot for them that they had to.
"I think these five weeks we've been through will be a blessing in disguise -- you find out a lot about people.
"What I've found out about our players and staff is we've got a really tough group."
Rookie Jack Underhill belted Alec Macdonald with a contender for hit of the season and Marcelo Montoya hammered Storm fullback Sua Fa'alogo.
In a side missing captain Stephen Crichton and with fullback Conor Tracey a late withdrawal, stand-in fullback Jacob Kiraz and centre Bronson Xerri stood tall and both clocked up more than 200m each.
The running game of five-eighth Matt Burton caused Melbourne all sorts of problems and halves partner Lachlan Galvin recorded three try assists.
Leo got the Storm on the board after three minutes before a Kiraz blunder handed the sevens convert a second.
Lebanese international Kiraz had raced across to stop a Jahrome Hughes kick trickling out for a 40/20 but clawed the ball back in field but right into the path of Leo who raced in to score.
Canterbury hit back when Galvin found centre Enari Tuala with a cutout but a try to Josh King put the Storm 18-6 up at the break.
It looked to be too steep a hill for a Dogs side with a spluttering attack to climb.
But Sitili Tupouniua barged over two minutes into the second half and Rinakama followed him after Burton and Nick Meaney had traded penalties.
Burton's penalty goal made it 20-20 with less than 20 minutes to go but Melbourne's inability to hold the ball - they completed at just 50 per cent in the second half - brought Craig Bellamy's men undone.
"It's nothing new to be honest - our second halves have been really poor, not quite sure why and I wish I was," Bellamy said.
"We ain't getting run down -- we're getting steamrolled."
Rinakama went in on the left to put Canterbury ahead in the 72nd minute with Kiraz rounding out a successful return with a late barge-over.
The only blight on the night for Ciraldo was the fact Jacob Preston came off in the first half with an arm injury and did not return.
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