Brentford went out of the FA Cup in former Chelsea boss Frank Lampard’s first game as Everton manager.
On a positive note for the Bees, goalkeeper David Raya made his return to action after more than three months out with a knee injury.
And Josh Dasilva, fit again after a hip injury, came on as a second-half substitute for his first appearance for a year.
Raya wasn’t helped by some woeful Brentford defending at Goodison Park, where goals from Yerry Mina and Richarlison put the home side in control before Ivan Toney’s penalty gave the visitors hope.
Mason Holgate’s goal effectively sealed the win for the Merseysiders and Andros Townsend netted in stoppage time.
Mina put Everton ahead with a header from Demarai Gray’s corner and Richarlison volleyed in the second after being found by Allan.
Toney scored from the spot after being brought down by keeper Jordan Pickford, but another Gray corner led to Everton’s two-goal cushion being restored.
Brentford made a total mess of trying to clear Gray’s delivery and Holgate helped himself to a goal.
Townsend thumped in the fourth after being teed up by Alexi Iwobi’s lay-off.
Brentford (3-5-2): Raya; Bech, Ajer, Jansson; Roerslev (Dasilva 72), Norgaard, Jensen, Janelt (Baptiste 62), Henry (sub Stevens 83); Canos (Ghoddos 72), Toney.
Subs not used: Fernandez, Lossl, Onyeka, Oyegoke, Young-Coombes.