United were below par for much of the 90 minutes, but seemed to have stolen an unlikely three points when Mason Mount converted his first goal for the club in the 96th minute.
However, almost immediately after play restarted, Brentford levelled things up, when Kristoffer Ajer slotted home from inside the area.
It was a devastating blow for the Reds, who were desperate to respond to victories earlier in the day for fellow top-four rivals Aston Villa and Tottenham Hotspur, but Brentford provided stern opposition and enjoyed far more attempts on goal over the course of the evening.