Substitute Leandro Trossard scored his first goal for Arsenal but the Premier League leaders missed the chance to move eight points clear at the top as Ivan Toney earned resilient Brentford a deserved point.
After a goalless first half in which the Bees hit the woodwork through Toney, the Gunners took the lead when Trossard struck at the back post four minutes after coming off the bench.
But Brentford got the reward their excellent away performance deserved when Toney nodded in Christian Norgaard's cross from close range.
There was a lengthy check by the video assistant referee for a possible offside in the build-up but the goal was eventually confirmed.
Arsenal raised the tempo in the closing stages - including seven minutes of added time - as they searched for a winner but Brentford completed an excellent all-round defensive display by holding firm for a point.
Arsenal face Manchester City - six points behind before their game against Aston Villa - in a top-of-the table showdown on 15 February.
If Pep Guardiola's side win on Sunday afternoon, they would reduce the deficit to three by the time the top two meet.