Bryan Mbeumo and Yoane Wissa got the goals for the Bees, who had left out England international Toney over speculation surrounding his future.
Toney has less than a year left to run on his contract with the London club and is attracting interest from Saudi clubs after his role in helping England to the Euro 2024 final.
Brentford boss Thomas Frank said pre-match his side had shown last season they can cope without Toney -- who missed much of last term due to a betting ban.
Marc Guehi did captain Crystal Palace despite the interest in him shown by Newcastle.
The England defender had an outstanding Euros but a moment to forget for Brentford's opening goal.
Mbeumo raced onto Wissa's pass and cut inside Guehi before firing into the far corner.
Palace ended last season in sensational form under Oliver Glasner and will feel hard done by not to have earned at least a point.
Eberechi Eze had a brilliantly executed near post free-kick harshly ruled out for a foul by Will Hughes when the score was still level at 0-0.
A bright Palace start to the second half was rewarded when Ethan Pinnock turned Daniel Munoz's header into his own goal.
Seconds later, Odsonne Edouard slotted home Eze's pass only to be denied by a marginal offside decision.
Instead it was Brentford who grabbed the vital third goal.
Dean Henderson could only parry Nathan Collins' shot straight into the path of Wissa, who bundled home.
Eze was twice denied by Mark Flekken in the closing stages but Brentford held out for an impressive three points.
Champions Manchester City begin the defence of their Premier League title later on Sunday with a trip to face Chelsea in Enzo Maresca's first match in charge of the Blues.
