Kevin Schade's brilliant solo goal put Brentford ahead but an equaliser from Joachim Andersen was enough to seal a 1-1 draw at the Gtech Community Stadium.
Schade's run down the left saw him beat two men to burst into the area and fire hard and high past Sam Johnstone 29 minutes in.
But Andersen squeezed a finish past Mark Flekken in the 76th minute on an afternoon where the goalkeeper's cat-like reflexes kept out the visitors on multiple occasions.
Brentford remain unbeaten after three games this season and sit on five points, while Palace have four.