Damian Duff opened the scoring for the home side after only five minutes, but the Polish champions equalised soon after through a Andras Kirm strike.
The result was sown up by goals either side of half time, as striker Andrew Johnson bagged a brace, before Steven Sidwell completed the rout.
The win means that the Cottagers are in second place in Group K behind leaders Twente and four points above the side they just beat and Danish outfit OB Odense.
After the game manager Martin Jol was full of praise for his team.
“We scored early so that was good, but then we lost the ball in midfield [and they scored],” the Dutch coach told Sky Sports.
“That said, we scored some great goals. The second goal was amazing and the third one was a clever one.
“If you could come up with ideas like that every week you would be like Real Madrid in the golden days,” he stated.
The former Spurs boss also praised goalscorer Johnson, who continues to find the net for the Craven Cottage side on a regular basis.
“He scored a hat-trick against QPR and if he could do that every game it would be unbelievable, but we are not doing that.
“It was nice to see him score goals because his second goal was completely different to his first so that is good for a striker. It gives him a lot of confidence,” he concluded.
Fulham now host London rivals Tottenham on Sunday, and will look to take momentum from this comfortable victory.
By Gareth McKnight