The board went up to show nine minutes of stoppage time but there would be no dramatic late winner for Arsenal.
Mikel Arteta's side thought they had pulled off the comeback when Eddie Nketiah, on at half-time for Leandro Trossard, added to Bukayo Saka's penalty, cancelling out Andreas Pereira's first-minute opener.
But Fulham were to be the orchestrators of the drama in north London as Joao Palhinha struck four minutes from time to secure a valiant point.
Marco Silva and the travelling fans feared the worst when Calvin Bassey was sent off for two bookable offences, but it only galvanised Fulham through to the final whistle.