Top scorer Clint Dempsey netted his eighth and ninth goals of the season as the Cottagers made it three wins in five to put daylight between themselves and the drop zone.
The match was the third tempestuous affair between the sides this season and Potters captain Ryan Shawcross was sent off after bundling over Dempsey in the box.
The American, who had already given his side a half-time lead, stepped up to convert the resulting penalty and seal a comfortable victory.
The opposing managers had refused to shake hands following their two previous meetings this season.
But Fulham boss Mark Hughes was keen to end the feud and duly made the first move as he greeted Tony Pulis before the game, and they were again on favourable terms after the game.