Stand-in Clarets skipper James Tarkowski, who took the armband in the absence of the injured Ben Mee, gave the hosts the lead on the stroke of half-time.
The defender poked the ball past Dean Henderson from close range after Jay Rodriguez had flicked on Dwight McNeil's set-piece.
John Egan, who moved to Brentford following Tarkowski's departure in 2016, levelled with 10 minutes remaining when firing the ball into the top corner.
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John Egan, who moved to Brentford following Tarkowski's departure in 2016, levelled with 10 minutes remaining when firing the ball into the top corner.