Jamaica international striker Fuller tore Albion apart in eight minutes of first-half mayhem.
He scored the first goal, saw his cross turned into his own net by Albion midfielder Jonathan Greening and then set-up the third for Jon Parkin as Stoke followed up last weekend's success against Leicester City with another emphatic victory.
All Albion had to show for their efforts was a 74th minute consolation strike when Jason Koumas saw his 20-yard drive deflected past goalkeeper Steve Simonsen.
But the writing had been on the wall for Albion by the 22nd minute when Parkin scored Stoke's third.
Albion's shell-shocked defence, and Sam Sodje in particular, had no answer to Fuller as Stoke's extra physical power proved to be crucial.
Albion are now facing a real battle to make the play-offs - a far cry from the end of February when then they were top of the table.
But since reaching that lofty position, they have been in freefall - collecting just five points from their last seven games.
Albion's downfall was started by Sodje's misplaced clearance in the 14th minute as Fuller latched on to the loose ball and easily held off the challenge of Paul Robinson before drilling home his tenth goal of the season.
Fuller's front-line partner Mamady Sidibe was injured in the build-up to the goal and was stretchered off, but that proved to be no handicap to Stoke as his replacement Parkin quickly made his presence felt.
When Fuller crossed from the left, Parkin pressured Greening into turning the ball into his own net.
Fuller repeated the trick again two minutes later, this time holding off Sodje and Paul McShane before crossing for the unmarked Parkin to pounce from 12 yards.
Albion were simply left stunned but did their best to rally before half-time with Nathan Ellington hitting the bar from 25 yards, Sodje heading wide and Koumas being denied by Simonsen.