The Cottagers struggled to create much inside the first 90 minutes but extra time strikes from Bobby Reid and Neeskens Kebano proved the difference on the night.
Rangers were the better side in the opening stages as Illias Chair and Bright Samuel both tested Marek Rodak before the break.
The expected Fulham response never really got going in the second period with Joe Bryan’s snapshot the only real test for Seny Dieng.
But the Cottagers looked refreshed in the extra 30 minutes as Scott Parker’s charges showed their top-flight edge.
Reid proved the key in the door for Parker as he lashed home the breakthrough goal from outside the box before Kebano tucked home Josh Onomah’s pass to seal it.
Full Time at Loftus Road it’s QPR 0 Fulham 2