United, top of the Sky Bet Championship and 11 points clear of third place just two months ago, have seen that lead evaporate over the last 10 matches.
But Liam Cooper equalised to secure a valuable point for a side who had lost four of their previous five matches.
However, they will still find themselves outside the automatic promotion spots in 24 hours if Fulham pick up a win at Millwall.
Leeds arrived in west London with a terrible history against the Bees, having not won at Griffin Park since 1950, while their record in the capital this season reads: played four, lost four.
Also fresh in the memory was their defeat at Brentford, in their third last match of last season, which derailed that campaign's promotion push.
But Brentford began to make inroads onto the Leeds half, first when Christian Norgaard fired narrowly wide from 18 yards out.
Moments later the hosts were handed the lead after Casilla slipped and let Cooper's backpass roll under his foot, allowing Benrahma to tap home at the far post.
It was an awful error from the former Real Madrid keeper, whose place in the side is already under scrutiny following some recent shaky performances.
Raya was back in action to tip Pablo Hernandez's fierce volley over the crossbar, but he was partly culpable when Cooper equalised for Leeds seven minutes before the interval.
Raya came for, and missed, a corner and as the Bees failed to clear their lines the ball dropped to the Whites skipper who leathered it into the back of the net.
Bielsa threw on January recruit Jean-Kevin Augustin for the final 15 minutes but the closest they came to a winner was a Hernandez effort which was deflected over the crossbar.