Noni Madueke put Arsenal in front on the hour mark with a fine header.
But the hosts were back on terms only 10 minutes later when Keane Lewis-Potter struck following Michael Kayode's long throw.
Following their equaliser, Brentford, who knew a win would take them above Liverpool in the table, looked the more likely to score with Igor Thiago wasting a golden chance in stoppage time.
However, substitute Gabriel Martinelli might have then won it for Arsenal only to be denied by Caoimhin Kelleher in a frantic end to the match.
Just four days ago at Liverpool, Pep Guardiola's side were six minutes away from falling nine points behind their rivals, but they are now within striking range.
And Arsenal, runners-up for the past three seasons, will still have to visit the Etihad Stadium in April as they look to end their 22-year wait for the title.
Following City's comfortable 3-0 win against Fulham a day earlier, the onus was on Arsenal to restore their six-point advantage.
But for much of the game, the Gunners - without the calming presence of William Saliba through illness - were well below their best.
Indeed, they could easily have fallen behind midway through the opening period when David Raya's wayward throw to Declan Rice was picked up by Mathias Jensen.
With Rice on the turf, the Brentford captain had the time and space to pick his man, and he delivered a pinpoint cross to Thiago who looked destined to score.
However, Raya atoned for his howler with a brilliant one-handed save to deny Thiago's goalbound header.
Brentford hustled and hurried Arsenal and Mikel Arteta's players headed for the interval without creating a chance of note.
Eberechi Eze was handed his first league start in two months and a day here, but he was back warming the bench after an ineffective 45 minutes with captain Martin Odegaard - absent for the past two games through injury - sent on in his place.
Arsenal started the second half with greater intent, but the hour mark was fast approaching with Kelleher still a bystander in the Brentford goal.
Odegaard then blazed well over. "Top of the league, you're having a laugh" goaded the home supporters.
But it was the visiting section in full voice just moments later, when Madueke delivered the breakthrough. Kayode's clearance fell only to Piero Hincapie and Madueke header his sumptuous cross home.
Arsenal might have been expected to close out the three points but Brentford had other ideas.
Lewis-Potter headed a decent chance from Jensen's corner wide. Thiago hit Arsenal on the counter-attack, but Raya was equal to his effort.
Gabriel was then needed to divert Kayode's stinger from danger with a diving header.
Brentford were suddenly looking dangerous, and they were back on level terms with 19 minutes left. Sepp Van Den Berg rose highest from Kayode's menacing long throw and Lewis-Potter launched himself at the flick-on with an unstoppable header.
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