- Mathias Jensen (28')
- Abdoulaye Doucouré (6')
- James Tarkowski (67')
- Dominic Calvert-Lewin (71')
After a first half of many missed opportunities ended 1-1, Tarkowski headed in off Dwight McNeil's corner after 67 minutes.
England forward Dominic Calvert-Lewis, who came on just past the hour mark, then made it 3-1 in the 71st off the leg of goalkeeper Mark Flekken, as Everton emphatically avoided sinking to their worst start to a season since 1958.
"You can see the emotion at the end with the lads and the fans. It's been a tough start to the season," said Calvert-Lewin.
The victory lifted the transformed Toffees out of the drop zone and up to 15th with four points and left Brentford, now 12th on six and still waiting for their first home win of the season.
Everton manager Sean Dyche, who had urged his men in the run-up to "play with a smile", felt they had pushed back some of the negativity.
"The signs have been there but you've got to change the storyline, you've got to score goals, you've got to take your chances," he said.
The visitors could have been two or three goals up, with Vitaliy Mykolenko shooting straight at Flekken in the 21st and Doucoure hitting the crossbar seven minutes later, but Danish international Mathias Jensen levelled in the 28th.
His low effort that went in off the far post sparked some life into a listless Brentford, who had record signing Kevin Schade ruled out just before the start with a warm-up injury and Keane Lewis-Potter coming into the side as replacement up front.
The home fans had a nervous wait for a VAR check for a possible offside by Yoane Wissa before Jensen's goal was given.
"Everton deserved to win, we performed badly," said Brentford manager Thomas Frank, whose side next host Arsenal in a League Cup third round match on Wednesday.
"We performed very well the first five games of the season, today was a bad one, very unlike this group of fantastic players to perform like that."
Frank said his side had lost the set-piece battle, despite being prepared for it, and were also "simply not good enough on the ball" with misplaced passes and poor touch especially in the first half.
- Michael Oliver
|Brighton & Hove Albion||15||7||4||4||+5||25|
|West Ham United||14||6||3||5||0||21|