Leeds were involved in another eye-catching encounter in their first top-flight home match for 16 years.
After losing 4-3 at champions Liverpool on the opening weekend, Helda Costa fired Marcelo Bielsa's free-scoring side ahead in the fifth minute, blasting home from a tight angle following Kalvin Philips' corner.
Fulham striker Aleksandar Mitrovic equalised from the penalty spot in the 35th minute after a foul on Joe Bryan. Bryan was penalised himself for his shove on Patrick Bamford and Mateusz Klich restored Leeds' advantage with a 40th-minute spot-kick.
In the 51st minute, Klich's fine pass into the area carved Fulham's defence open and Patrick Bamford steered a right-footed finish into the bottom corner.
Leeds struck again six minutes later with a superb second goal for Costa, who slammed home following Bamford's superb run and cross.
Fulham pulled one back in the 62nd minute through Bobby Decordova-Reid and Mitrovic's towering header four minutes later set up a tense finale, but the promoted Cottagers fell to a second successive defeat.