The Storm surged home at AAMI Park to secure a 30-22 victory to stretch the winning streak over their trans-Tasman rivals to 14 games.
The change-room erupted post-match with news the giant prop had inked a new contract with Melbourne, resisting huge offers from the Dolphins and Rugby Australia.
"It's massive for our club," said coach Craig Bellamy on the re-signing.
"We all know what a talent he is - he probably turned the game for us when he came on.
"He's unique in what he can do on the footy field."
Despite the Warriors emptying their bench through injury, the match was in the balance until star Storm hooker Harry Grant muscled over the line with four minutes remaining.
Warriors skipper Tohu Harris was assisted from the ground late in the first half, re-injuring his left knee .
They also lost Charnze Nicoll-Klokstad and Bayley Sironen to head knocks and Jazz Tevaga to a possible Achilles injury.
The Warriors started strong, quickly erasing memories of last year's 60-point horror show to lead 18-6 with Jackson Ford, Dallin Watene-Zelezniak and Addin Fonua-Blake finding gaping holes in the Storm defence.
But the game changed in the 21st minute with prop Asofa-Solomona coming off the bench in his first match since suffering a knee injury in round two.
He immediately put the home side on the front foot with a series of barn-storming runs, the type that caught the eye of Wallabies coach Eddie Jones.
The Kiwi international finished with 148-run metres from 14 runs and 20 tackles in his 59 minutes.
Cameron Munster, who booted a brilliant 40-20 to set up the Storm's first try scored by Justin Olam, then dived over himself in the 34th minute to close the gap to 18-12.
Warriors playmaker Dylan Walker was sin-binned and put on report for an alleged high shot that saw Storm back-rower Eli Katoa fail a HIA.
Despite being down a man the Warriors were first to score in the second half when Watene-Zelezniak collected his second, but that was all the visitors had to celebrate.
With the Warriors down on troops, the Storm roared back with fullback Nick Meaney taking full advantage of two kicks into the in-goal before Grant iced the win.