The win left Fulham third in Group E, one point behind FC Basel and two behind first-place Roma with one game to play.
Fulham must win at FC Basel on the final day of group play on Dec. 16 to advance to the knockout phase.
Manager Roy Hodgson had Damien Duff, Aaron Hughes and Dempsey on the bench to start the game. Cottagers have a key English Premier League match against against Sunderland on Sunday.
"The Premier League is the major concern and the Europa League comes second to that," Hodgson said. "I don't think the fans will hold anything against us for our performances in this competition. They know when we go to Basel we will be doing our very best."