Arsenal will be disappointed with the manner of this draw despite Brentford only losing twice at home this season.
The Gunners struggled to break down their resolute opponents in the first half, with centre-back Gabriel Magalhaes having their best opportunity from a corner.
Mikel Arteta gave England international Eberechi Eze his first start in the league since December, but the number 10 did not take his chance with Kai Havertz out of the squad and was replaced by captain Martin Odegaard at half-time.
It looked as though Noni Madueke's header was going to give the Gunners an important victory as they look to keep the chasing pack at bay but they were unable to keep out Brentford, who like Arsenal are one of the league's best sides at set-pieces.
The Gunners will be accused of starting to show signs of struggling under the pressure of trying to win a first title since 2004, but they face Wolves on Wednesday and can move seven points clear of Manchester City if they beat the league's bottom side.
However, City have produced incredible runs of form to chase down titles in previous years and Arsenal have finished second for three successive seasons.
With 12 games to go, history does not favour Arsenal with their end-of-season form.
In the past five seasons, only on one occasion have Arsenal won 10 of their final 12 Premier League matches in a campaign.
In those seasons, the Gunners have never won more points in their final 12 games than the team that went on to win the title.
Former Arsenal defender Martin Keown said on TNT Sports: "That's what people were shouting at me as I was coming off the pitch, 'Man City are coming to get you', but at the end of the day Arsenal are four points clear.
"You get knocked down, you get up again. Let's see who the fighters are and let's see who is going to win this. They could have put down a big marker if they won the match, but it never looked like that was going to be the case."
In two of their three second-placed finishes in recent years, Arsenal have finished behind Manchester City, which is why the talk about this title race carries so many emotional scars for supporters.
"What Man City have got is the know-how and the recent history behind them," Peter Crouch added on TNT.
"That can lead to nervous tensions around the stadium, certainly around the back end of the season.
"Having someone like Man City and Pep behind you, you are always going to be looking over your shoulder. But you would much rather be in Arsenal's position."