Eddie Nketiah's goal late in stoppage time for Arsenal delivered a major blow to Fulham's already slim Premier League survival hopes.
Until Nketiah's 97th-minute effort, Josh Maja's second-half penalty had looked likely to give the Cottagers a valuable three points in their battle against relegation.
The on-loan Bordeaux forward converted from the spot after Mario Lemina was fouled by Arsenal's Brazilian defender Gabriel.
It was Fulham's only shot on target and put them on course for their first away league win against the Gunners in 29 attempts.
However, Scott Parker's side buckled under some late Arsenal pressure, with Nketiah tapping in after Dani Ceballos' shot was initially saved by Fulham goalkeeper Alphonse Areola.
The result leaves Fulham six points from safety, but with the added disadvantage of having played two games more than both Brighton and Burnley - the sides directly above them.
In a game of few clear-cut chances Arsenal, who remain ninth, merited their point.
Mikel Arteta's side had Ceballos' first-half goal disallowed after Bukayo Saka had strayed fractionally offside, while Gabriel Martinelli also found the back of the visitors' net after the whistle had gone for offside against Emile Smith Rowe.
However, in the last minute of the game, Arsenal substitute Nketiah rescued a point after reacting quickest to Areola's save inside the box.