The Jamaica international finished off Palace after Jon Parkin had scored for the third game in succession to lift the play-off chasing Potters to within one point of a much-coveted sixth spot.
The hosts were made to sweat on maximum points after Gabriel Zakuani's hashed goal-line clearance reduced the deficit and set up a nerve-wracking second half.
Judging by the error-laden first-half display, the busy Easter weekend fixture pile-up had taken its toll despite both managers' efforts to freshen things up.
Two changes apiece from both parties' Saturday team-sheets couldn't mask the fatigue in the opening half-an-hour.
Palace wasted two golden opportunities early on when Gary Borrowdale flashed wide before a heavy touch from Clinton Morrison allowed City to regroup and snuff out the danger.
And the Eagles were left bemoaning their lack of composure when Stoke bagged a quick-fire first-half brace which owed more to the Eagles' weary rearguard then any attacking guile.
Parkin powered a well-hit volley past Gabor Kiraly's outspread frame from range after being given an age to twist his marker into the turf, before Fuller turned on his turbo to jet into the danger-zone.
He jinked past two challenges with some ease before finding the target from a tight angle despite Mark Hudson's attempts to clear from the line.
Lee Hendrie, returning to the starting line-up, could have added a third to put City into the comfort zone but the hosts' half-time advantage was reduced on the half-hour mark.
Mark Kennedy's lofted corner was met by Leon Cort's thumping header which was somehow bundled over the line when Zakuani's attempted clearance found the bottom corner.
But having beaten a play-off contender in their weekend's exploits, Palace weren't to be overawed by another Premiership hopeful asserting their lofty league stature.
The Eagles had plundered three at Preston's expense just 48 hours earlier and they could have had two more at the Britannia Stadium were it not for the sturdy palms of Steve Simonsen.
The cat-like stopper beat back a goal-bound Paul Ifill drive 18 minutes after the restart before getting a strong hand on Tom Soares' fierce 20-yard drive as the Eagles began to soar.
But as the visitors turned the screw, Stoke sprang a succession of counter-attacks which should have had the Londoners level.
But Liam Lawrence somehow managed to hook over from underneath the bar after Hendrie's good work inside the box left Kiraly absent from his station and his goal exposed.