Storm halfback Jahrome Hughes took charge with Cameron Munster and Harry Grant away on State of Origin duty and his composure in attack was the difference between the understrength sides.
The match was the Tigers' first since injured Luke Brooks rejected their contract offer and their directionless attack reiterated the urgent need to finalise a halves pairing for 2024.
In the absence of Brooks and hooker Api Koroisau, makeshift halves pairing Starford To'a and Brandon Wakeham were incapable of turning brief periods of dominance into points.
"I'm not going to whinge about our spine disintegrating after last game," Tigers coach Tim Sheens said.
"It had something to do with it ... but in the big moments, we'd drop the ball or make a mistake, they'd defuse a kick, and they'll make you pay."
The loss was Wests' third in a row, leaving their promising May firmly in the past and consigning them to last spot on the ladder.
But in his 116th first-grade game, Twal put to rest one of the NRL's longest-running gags.
Wakeham's cross-field kick ricocheted from Melbourne hands onto the turf midway through the first half and Twal reached out to ground it just one minute after coming on from the bench.
Twal's teammates immediately swarmed him and referee Ziggy Przeklasa-Adamski struggled to suppress a smile as he awarded the try.
Cheers of 'Twally' rang out across Campbelltown Stadium.
"It's been a long seven or eight years, playing week in and week out and never getting a try," Twal said.
"I've found the humour in it.
"It was a bit of a bittersweet moment, I would have much rather come away with the result.
"But it was good to get the monkey off my back."
The try clearly encouraged the Tigers but the Storm were patient and claimed a 14-6 halftime lead thanks to Hughes and his golden boot.
He put a bomb up for Warbrick's second try and then dribbled a grubberkick through for Tyran Wishart, whose first try in 22 NRL games wasn't quite as popular with the crowd as Twal's.
Warbrick's other three tries were simpler, coming as the Storm shifted the ball right through hands to bamboozle the laggard defence.
"(Warbrick) is having one hell of a year," Bellamy said.
"It wasn't a polished win but it was a win and we will take that every day of the week, and obviously with Origin at the moment.
"I was really happy with the way our guys played, especially defensively."
The Storm would have won more convincingly had Nick Meaney brought his kicking boots; the fullback nailed only two of six attempts at goal.
"Tonight it didn't cost us but I'm sure he'll get the kicking tee out during the week and do some practice," Bellamy said.
Nelson Asofa-Solomona could attract scrutiny from the match review committee for striking stand-in Tigers captain John Bateman with an open palm off the ball in the second half.
Bateman appeared to shove the big Storm forward as he attempted to play the ball, prompting the moment of rage and ensuing melee. Przeklasa-Adamski permitted both men to remain afield.
"It's part and parcel of the game," Bateman said of the dust-up.
Melbourne's Tom Eisenhuth was placed on report for a crusher tackle on To'a and could join Asofa-Solomona on the charge sheet.
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