In the battle of two of the newly promoted teams, Leeds took an early lead at Elland Road when Hélder Costa lashed in off the crossbar from a tight angle.
Fulham then equalised when Leeds defender Robin Koch gave away his second penalty of the season, and Aleksandar Mitrović coolly dispatched from the spot.
But just minutes later, Leeds were awarded a penalty for a Joe Bryan push on Patrick Bamford, and Mateusz Klich made it 2-1.
And five minutes into the second half, Bamford slotted past Alphonse Areola to make it 3-1 to the hosts.
Seven minutes later it was 4-1 thanks to a lovely finish from Costa for his second of the game.
Fulham did then pull a goal back when Bobby Decordova-Reid fired low into the bottom corner for 4-2.
And it was soon 4-3 when Mitrović rose highest to power a header past Illan Meslier.
But that was how it finished.