Extra-time goals by Bobby Decordova-Reid and Neeskens Kebano took Fulham through to the FA Cup fourth round.
Decordova-Reid broke the deadlock in the west London derby by firing into the corner of the net after exchanging passes with Aleksandar Mitrovic near the edge of the penalty area.
Kebano sealed the Whites’ win by scoring three minutes later.
After Joe Bryan had done well on the left, Josh Onomah teed up Kebano and the Frenchman finished emphatically.
QPR strikers Lyndon Dykes and Macauley Bonne spurned glorious chances to score in normal time.
An unchallenged Bonne headed Ilias Chair’s corner over the bar and later volleyed wastefully over after being found by Todd Kane’s low cross from the right.
Dykes was guilty of an appalling miss in the second half, blasting woefully high and wide after Seny Dieng’s long ball left the Scot through on goal.
Fulham’s best opportunities before their breakthrough fell to Mitrovic, whose shot was cleared off the line by Yoann Barbet, and Bryan, who fired straight at keeper Dieng after being set up by Ruben Loftus-Cheek.
QPR: Dieng, Kane, Cameron (Masterson 90), Dickie, Barbet, Ball, Carroll (Bettache 81), Chair (Thomas 81), Osayi-Samuel (Hamalainen 90), Bonne (Kelman 73), Dykes.
Subs not used: Barnes, Adomah, Willock.
Fulham: Rodak, Aina, Ream, Kongolo (Hector 67), Tete (Robinson 90), Onomah, Reed (Kebano 78), Loftus-Cheek (Odoi 90), Bryan, Cavaleiro (Decordova-Reid (67), Mitrovic.
Subs not used: Fabri, Adarabioyo, Carvalho, Jasper.