Jesse Marsch’s side had the better chances and forced Brentford goalkeeper David Raya into several good saves at Elland Road.
Teenager Wilfried Gnonto, fresh from his double in the FA Cup win over Cardiff on Wednesday, had the best opening but his effort was kept out by Raya.
Brentford failed to produce a shot on target but kept their discipline in defence to keep Leeds out and extend their unbeaten record to eight successive games.
Bees forward Ivan Toney cut an isolated figure up front and his frustration boiled over with a tussle for possession with Robin Koch costing him a yellow card.
The point lifts Leeds up to 15th place, a point above the relegation zone, while Brentford move up to eighth.
Result suits Brentford but Leeds show signs of improvement
These two sides had produced 14 goals in their three Premier League meetings, but this one was lacking clear-cut opportunities at either end of the pitch.
Marsch and his Leeds side are under pressure and the stalemate means the hosts have only won once at Elland Road since August.
But this was a promising display as Leeds had more of the ball and produced five shots on target. Standing in their way was the in-form Raya, who made six saves to ensure a clean sheet for Thomas Frank’s side.
January signing Max Wober, making his first league start in place of injured captain Liam Cooper, produced the first attempt with a curling free-kick which went narrowly wide.
Rodrigo then forced Raya into an acrobatic save before the interval as Leeds upped the ante, but the final product was lacking.
When Gnonto was played in on the angle, the Italian’s well-struck effort was at a comfortable height for Raya to react and palm behind to safety.
Leeds’ intent against a side who have won their last three league games will have pleased the home crowd, but they lacked a clinical edge to turn one point into three and give themselves a greater safety cushion.
Brentford were resolute in their shape and were tough to break down, and a hard-earned point on the road keeps them in the hunt for European football.