The visitors put in an excellent defensive performance at Emirates Stadium and looked like they may knick all three points when Aleksandar Mitrovic gave them the lead in the 56th minute.
The Gunners are now back top of the Premier League after winning all four of their opening games this season.
Simon Collings was at Emirates Stadium to see Arsenal in action...
Aaron Ramsdale 7
Was having a really quiet game but then made a huge save to keep out Mitrovic’s header from a corner. Made another great save late on to deny Nathaniel Chalobah.
Ben White 7
Had another good game at right-back, where he is looking more settled as every week goes by. Made some strong, driving runs forward.
William Saliba 7
The Frenchman carried on his fine form with a solid performance here. Once again so composed on the ball and dealt well with Mitrovic’s physicality.
A crazy afternoon for the Brazilian. He made an absolute howler for the Fulham goal, but then scored Arsenal’s winner late on.
Kieran Tierney 6
Had a fairly solid game at left-back but couldn’t offer what Oleksandr Zinchenko does. Looked okay on the overlap, but struggled when tucking into midfield.
Martin Odegaard 8 | Star player
Arsenal’s goalscorer and their best player over the course of the 90 minutes. Had some lovely touches and passes in around the Fulham area.
Mohamed Elneny 6
Neat and tidy at the base of midfield as he kept things simple. Not a bad understudy for Thomas Partey, but lacks the Ghana international’s range of passing.
Granit Xhaka 7
Another good game from the midfielder, who is enjoying his best run of form since he joined Arsenal. Went close with an effort in the first-half.
Bukayo Saka 6
Still doesn’t look at his best and he had a frustrating afternoon. Missed a golden chance in the first-half, but did assist Odegaard’s goal.
Gabriel Jesus 6
Worked tirelessly, on and off the ball, but didn’t get much joy. Had a few sights of goal, however Fulham crowded him out well.
Gabriel Martinelli 6
Not at his blistering best but tried to make things happen out left. Got to the byline with the odd mazy run but his final ball was lacking.
Eddie Nketiah (Tierney 61’) 6
Off the bench and looked lively, offering Arsenal an added threat in behind. Missed a good chance from a Martinelli cut-back.
Takehiro Tomiyasu (Jesus 89’) N/A
Rob Holding (Odegaard 90’) N/A
Subs not used: Turner, Smith Rowe, Cedric, Vieira, Sambi Lokonga, Marquinhos