Bryan Mbeumo's penalty put the Bees in front after a VAR review confirmed Marc Guehi's encroachment in the penalty area. Kevin Schade then doubled the lead, but a late goal from Palace debutant Romain Esse made for a tense finale.
Five of the seven Premier League meetings between the teams had ended level, and there was little in the first half to suggest that would not be the case once again.
Mark Flekken produced a strong right-hand to keep out a fierce strike from Jean-Philippe Mateta inside 10 minutes, while at the other end, Yoane Wissa's low effort was tipped around the post by Dean Henderson and Mbeumo's free-kick whistled inches past the post..
Chances came at a premium, as illustrated by the combined Expected Goals total of 0.4 at the break - 0.2 xG each.
But it sparked into life around the hour. Eze's free-kick took a wicked deflection and hit the right-hand post with Flekken stranded, before the visitors were awarded a penalty when Will Hughes handled and Nathan Collins was brought down by Maxence Lacroix.
Mbeumo struck the post, to the delight of the hosts, but after a VAR review, it was determined that Guehi had encroached the penalty area and the Cameroon international would get a second chance - which he duly took.
The second Brentford needed came after 80 minutes, when the irrepressible Mikkel Damsgaard - who signed a new deal until 2030 earlier this week - planted a peach of a cross onto the head of Kevin Schade, who headed home.
Esse then scored with his first touch, just 119 seconds after entering the pitch, which set up a tense finale with nine minutes added on, but unfortunately for Palace it could not spark the goal they needed to force a point.