Martin Jol's side had won only one of their last 12 games but began 2013 with a bang against the club he graced as a player with Dimitar Berbatov giving the dominant visitors a 39th-minute lead when his shot evaded goalkeeper Ben Foster.
West Brom, riding high in seventh spot, improved markedly after the break and Belgium forward Romelu Lukaku increased speculation about a possible recall by parent club Chelsea this month by capping a superb display with a 49th-minute tap-in.
The hosts then hit the post twice but 12th-placed Fulham would not be denied and Swedish winger Kacaniklic expertly spun on the edge of the area before stroking the ball home 13 minutes into the second half.
Leaders Manchester United play at Wigan Athletic later (1500 GMT) when champions and second-placed Manchester City host Stoke City. (Writing by Mark Meadows; Editing by John Mehaffey)