The night's solitary League match went ahead in sub-zero temperatures and Stoke looked to have it in the bag after racing into a 3-0 lead at halftime.
Tuncay Sanli opened the scoring with a close-range header following a corner after 12 minutes.
Poor Fulham defending allowed Abdoulaye Faye to turn in a Matthew Etherington free kick after 34 minutes and a nice move ended with Mamady Sidibe slotting in the third.
Fulham pulled one back with a deflected Damien Duff goal and when Clint Dempsey looped in a 30-metre shot five minutes from time the home fans had to endure nervous moments before celebrating the end of a run of three successive defeats.
Stoke climbed to 10th in the table on 24 points, one place and three points behind Fulham.
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English Premier League weekend schedule