First-half goals from Ross McCormack and Shaun Hutchinson put the Cottagers in the driving seat, before Lasse Vigen Christensen and Cauley Woodrow, who netted from the penalty spot, sealed victory after the break.
The win moved Kit Symons’ side level with their opponents in the table after a second-successive win.
Marcus Bettinelli and Scott Parker returned to the Fulham side, while the visitors also made two changes, with Joe Mattock and Jose Semedo coming in.
The home side flew out of the blocks and forced a flurry of corners, with Hugo Rodallega and Hutchinson denied early on.
Nikolay Bodurov headed a McCormack free-kick over, while at the other end, Chris Maguire tried his luck from distance.
Tom Lees squandered a good chance for the visitors when he stabbed wide, but he made amends for his miss moments later when his vital interception denied Rodallega an open goal after Christensen had rounded Kieren Westwood.
Bettinelli was called into action when he dived low to his right to keep out Maguire’s well-struck drive, while Westwood did well to save from Rodallega after hesitation in the Wednesday defence.
The Owls grew into the game and Kostas Stafylidis was in the right place at the right time to scramble Stevie May’s flick off the line, while Lewis McGugan’s curling free-kick hit the side netting minutes later.
However, it was Fulham who broke the deadlock against the run of play on 34 minutes. Glenn Loovens was penalised for a foul on Seko Fofana at the edge of the box, and McCormack stepped up to curl a stunning free-kick into the top left-hand corner.
Jeremy Helan came close to an equaliser when he fired just wide, but the home side doubled their advantage in the 45th minute. The visitors gave away another cheap free-kick and Hutchinson stooped to head home Bryan Ruiz’s inswinging set-piece.
Wednesday boss Stuart Gray responded by bringing on Atdhe Nuhiu and Royston Drenthe at the beginning of the second half as they tried to salvage something from the game. The visitors dominated but failed to force Bettinelli into a save, with Nuhiu heading over and Maguire dragging a shot wide.
But Christensen put the game out of their reach in the 68th minute with a fine breakaway goal. Rodallega fed the young Dane, who shimmied his way through before slotting past Westwood with the aid of the post.
The clinical Cottagers took their foot off the gas after that but were denied the chance of a fourth when referee Andre Marriner waved away their penalty appeals after substitute Woodrow was brought down by Westwood.
However, Woodrow got his name on the scoresheet in stoppage-time from the spot after Claude Dielna scythed down McCormack.