First-half goals from Aboubakar Kamara and Bobby Decordova-Reid put the hosts in a comfortable position.
Anthony Knockaert had two chances to increase the lead but dragged his shot wide and hit the bar with a lob.
The fourth-round tie will be a repeat of last season's Championship play-off, won by the Cottagers.
Speaking about facing the Bees, manager Scott Parker said: "It's a derby in the next round of the cup so of course it's a big game for both sides.
"The last time we played, that game was certainly a lot bigger than the one we are going to be playing next week. That's not to put the game coming up down in any way, that's the reality.
"As always when it's a London derby and you're up against your rivals there's always a little bit more of an edge to it.
"We're looking forward to playing against a very, very good Brentford side, which they are."