The Storm kept their recent domination of the Roosters intact to string together a fifth-straight win in a performance set-up by Anderson's attacking and defensive heroics.
But the 24-year-old ended Saturday night's match writhing in pain on the ground after landing awkwardly when he attempted a chip-kick near the sideline in a bid to complete a hat-trick of tries.
Grant Anderson was the star of the show for Melbourne. (Scott Barbour/AAP PHOTOS)
The finish soured what was another clinical performance by the Storm, who completed a 10th win in their last 11 starts against the Roosters.
The ladder-leaders never trailed, surging out to a 10-0 lead, but the Roosters threatened late when Dominic Young, who struggled early in the match, gave the visitors some life when he crossed in the 67th minute.
Anderson pulled off a spectacular try-saving tackle when he prevented Young from scoring again seven minutes later.
That effort meant the Storm couldn't be beaten, with Sualauvi Faalogo coming off the bench in the dying stages to pull off a crowd-raising try.
Melbourne were missing captain Christian Welch but only had stand-in captain Harry Grant backing up from State of Origin III duties compared to the Roosters' four.
Jack Howarth scores a try for the Storm. (Scott Barbour/AAP PHOTOS)
In his first game back after serving a four-game suspension for his hit on Reece Walsh in Origin I, Roosters flyer Joseph-Aukuso Suaalii was placed on report for a knee lift on Storm winger Will Warbrick.
Suaalii has a history of raising his knees, copping a three-game ban last year and avoiding another suspension for the same charge in May in a match against the Warriors.
The Storm were denied what halfback Jahrome Hughes called "one of the best tries that never happened" in the first-half.
Hulking forward Josh King decided to put the ball on his boot, setting up Anderson perfectly in the corner to send the Storm crowd into delirium.Â
But the four-pointer was overruled after Elisea Katoa was deemed to have knocked the ball on before King got his kick away.
Jahrome Hughes sent a scare through the Storm camp when he clutched his leg in the second-half, but the halfback played out the match in a sign the injury might only be a corked thigh.
The result improved the Storm's season record to 14-3, while the Roosters sit fourth, three games adrift.
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