Brentford were beaten at home for the first time since April as three Everton goals saw the Toffees take the points in west London.
Abdoulaye Doucoure volleyed the away side in front after just six minutes, but the Bees were level before the half-hour mark thanks to Mathias Jensen’s third goal in four games.
However, the away side wrapped up the win with two goals in four second-half minutes courtesy of James Tarkowski and Dominic Calvert-Lewin.
Jensen levels after Doucoure opener
Brentford were forced into a pair of changes from last Saturday’s defeat at Newcastle United, and then a further change moments before kick-off.
Rico Henry missed out due to a knee injury while a muscle injury also sidelined Ben Mee. Mads Roerslev and Kevin Schade came in for the pair, with Aaron Hickey switching from right-back to left-back, but an injury picked up in the warm-up then forced Schade out, Keane Lewis-Potter his late replacement.
Everton’s one change saw James Garner replace Arnaud Danjuma on the right-hand side of their three-man forward line.
Lewis-Potter’s barnstorming early run was ended by Ashley Young; the veteran defender was booked inside a minute, Bryan Mbeumo curling the resulting free-kick wide from 25 yards.
The away side took the lead with their first attempt on goal. The ball was worked back in following a corner, Tarkowski nodding it down into the path of Doucoure to crack home on the half-volley from 12 yards.
Dwight McNeil drilled a shot inches wide of Mark Flekken’s left-hand upright, Amadou Onana flicked wide from a free-kick, and Vitaliy Mykolenko tamely shot straight at the Bees keeper as Everton threatened a second in the opening 20 minutes.
They, and Doucoure, thought they had their second after 27 minutes. A floated cross was taken down by the Everton midfielder in between Mads Roerslev and Nathan Collins but his shot from 10 yards struck the bar and bounced away to safety.
Despite being second best for the opening half-hour, Brentford managed to get themselves back on level terms through Jensen.
The midfielder started the move, which included Wissa, Bryan Mbuemo and Vitaly Janelt, with a neat flick around the corner, and finished it with a powerful low drive that found the back of the net via Jordan Pickford’s fingertips and the inside of the post.
VAR checked the goal as Wissa had been offside in the build-up, but it was decided that it wasn’t interfering with play so it stood.
Hickey had a shot blocked while, at the other end, Beto - who proved a handful all evening - scooped over Flekken and wide after collecting a low pass on the right side of the box.
Lewis-Potter diverted Mbeumo’s low cross wide at the back post under pressure from Tarkowski, Idrissa Gueye shot over, and Beto dragged a shot wide as the sides went in level.
Quickfire double secures win for visitors
The opening stages of the second half didn’t see much in the way of goalmouth action but Everton slowly started to turn the screw as the half wore on.
Dominating possession and forcing Brentford deeper into their own half, Everton had those few chances that were created.
Flekken dealt with McNeil’s tame shot from the edge of the box, Onana nodded wide, and Beto flicked a header off target before Everton took total control with two goals in four minutes.
Tarkowski netted the first of those, guiding a close-range header inside the far post from McNeil’s corner, and Dominic Calvert-Lewin got the second, collecting Garner's through ball and squeezing it under Flekken and home.
In between those goals, Ethan Pinnock, Christian Norgaard and Wissa were all denied during a goalmouth scramble which saw important blocks made by Tarkowski, Pickford and Doucoure.
Needing to find two goals in the final 20 minutes for a point, Brentford’s attacking efforts were stifled by Everton’s well-drilled back line.
The Bees’ day was summed up when Pickford’s poor clearance landed straight at Saman Ghoddos’ feet but he found referee Michael Oliver in his way when he attempted to shoot into an empty net from 35 yards.
Mbeumo helped Ghoddos’ deep cross straight into Pickford’s arms and Kristoffer Ajer looped a header over the bar from Mbeumo’s free-kick, but they were rare openings as Everton saw out the closing stages without real alarm to take the points.
Brentford: Flekken; Roerslev (Ajer 61), Collins, Pinnock, Hickey (Ghoddos 73); Norgaard, Janelt (Onyeka 62), Jensen; Mbeumo, Lewis-Potter (Olakigbe 89), Wissa
Subs not used: Strakosha, Balcombe, Zanka, Yarmoliuk, Brierley
Everton: Pickford; Young, Branthwaite, Tarkowski, Mykolenko; Gueye, Onana (Danjuma 77), Doucoure; Garner, McNeil, Beto (Calvert-Lewin 63)
Subs not used: Virginia, Patterson, Keane, Godfrey, Chermiti, Hunt, Dobbin
Frank identifies two areas to look into after Toffees loss
After Everton scored from two set-pieces on Saturday evening, that is one of two specific areas Thomas Frank wants to look into after the defeat against the Toffees.
“I think that Everton deserved to win," Frank said. "The first five games we played this season, we performed very well - this was a bad performance. We need to learn from that, move forward and bounce back.
“What this group of fantastic players have done very well over all the years I’ve been in charge here is that, after a bad performance, they’ve bounced back. So I expect that will happen on Wednesday against Arsenal.”
He added: "Everything that Everton came with didn't surprise us. We expected everything, we just handled it poorly. We just didn't deal very well with it.
“There are two things, besides the bad performance, that we need to look into: one is defensive set-pieces, obviously we conceded two goals and we weren’t on top of them.
“Secondly, is our quality and decision-making on the ball, especially in the first half. We were throwing the ball away way, way too easy with touches, passes and decisions.”
Norgaard on 'difficult' defeat
Brentford captain Christian Norgaard wants the Bees to bounce straight back after what he described as their 'worst' performance of the season so far on Saturday night.
The Bees lost 3-1 to Everton, despite Mathias Jensen’s goal in the first half at Gtech Community Stadium.
“It’s a difficult one to take,” said Norgaard. “So far, our performances have been really solid this season but this one was the worst so far.
"We were deservedly beaten and I think Everton deserved the three points.”
The Toffees scored after just six minutes but the midfielder doesn’t believe that set Brentford back.
“We came back and got the equaliser as well,” he said. “Until their 2-1 goal, I thought it was a very even game. I actually felt this was a classic or typical Premier League game today until their second goal, which we didn’t manage to come back from.
“It’s a tough one to take right now but we have to look forward, it’s still early stages of the season. We’ve seen a lot of positives so far in the games we have played but obviously today’s performance was not one to be proud of.”