Sarr nearly got Palace's third goal just seconds after the restart, going through one-on-one and beating Kelleher – only to be denied at the last by the post.
Brentford still had their moments. Kristoffer Ajer should have really done better with a header at the back post, but planted his effort straight at Henderson.
The Bees made a triple substitution in an effort to try and find a way back into the contest, with Keane Lewis-Potter, Vitaly Janelt and Mathias Jensen all introduced.
But it was their fourth substitute Reiss Nelson, who actually forced Henderson into action – the Palace No.1 making an excellent diving save to keep the score at 2-0.
It was the first time he had really been tested in the second-half and the Palace stopper responded magnificently.
In truth, that was as close as Brentford would come. Henderson made some comfortable catches in the dying minutes, as Palace saw out the game in relative comfort.
The Eagles now turn attention back towards Europe. AZ Alkmaar are the visitors on Thursday in the UEFA Conference League, before a showdown with Brighton and Hove Albion next Sunday.
A very big week for Palace, got the perfect start.
Palace: Henderson (GK), Richards, Lacroix, Guéhi, Muñoz, Kamada (Hughes, 78), Lerma, Mitchell, Sarr, Pino (Devenny, 78), Mateta (Canvot, 89)
Subs: Benítez (GK), Clyne, Sosa, Cardines, Esse, Uche.
Brentford: Kelleher (GK), Kayode (Lewis-Potter, 68), Collins, Van den Berg, Ajer, Yarmoliuk (Janelt, 68), Henderson (Carvalho, 86), Ouattara (Nelson, 75), Damsgaard (Jensen, 68), Schade, Igor Thiago
Subs: Valdimarsson (GK), Henry, Pinnock, Onyeka.
