Arsenal made to a similarly disastrous start when Andreas Pereira pounced on Bukayo Saka’s poor pass to catch Aaron Ramsdale off his line in the first minute at the Emirates.
Fulham’s rearguard held out for more than 70 minutes, but their resistence was finally broken when Saka levelled from the penalty spot.
Two goals in two minutes looked to have turned the game around as substitute Eddie Nketiah slotted home Fabio Vieira’s inviting cross.
Fulham’s Calvin Bassey was then sent-off for a second bookable offence.
But the 10 men salvaged a point when Joao Palhinha swept home a corner three minutes from time.