In what was an excellent first-half performance from Slaven Bilic’s side, the Baggies took the lead through an outstanding Grady Diangana goal.
Dominic Calvert Lewin - who went on to score a hat-trick - pulled the hosts level just past the half-hour mark when he back-heeled in Richarlison’s header.
The goal was initially ruled out with the striker in an offside position. But VAR showed Richarlison’s header took a slight deflection off Darnell Furlong andstood.
Everton took the lead on the stroke of half-time through a fantastic 25-yard strike from James Rodriguez.
But chaos then ensued with Kieran Gibbs shoving the forward in the face shortly after the re-start.
Referee Mike Dean had no choice but to send him off. Bilic was then also given his marching orders when he confronted the official during the interval.
Despite being a man down, Albion hauled themselves level shortly after the restart through a stunning Matheus Pereira free-kick.
But two more goals from Calvert-Lewin and a Michael Keane strike saw Carlo Ancelotti’s side comfortably grab the points.
Bilic said in his pre-match press conference that he had been pleased with how his players performed for the best part of an hour against Leicester.
And that led to the boss naming the same starting line-up for the trip to Liverpool with the Baggies once again in a 3-4-3 system.
It saw Kieran Gibbs and Darnell Furlong effectively operating as wing-backs giving Albion a back five when they didn't have the ball.
Up front, Callum Robinson was the central striker with Diangana and Pereira on the wings.
The only surprise selections came on the bench with new recruit Conor Gallagher absent from the matchday 18 along with Charlie Austin and Kamil Grosicki.
Everton named the same team that opened the season with a 1-0 win at Tottenham.
Lining up in a 4-3-3 formation, Calvert-Lewin was the lone centre-forward with Rodriguez on the right and Richarlison on the left.
In what proved a truly incredible first-half, the tone was set right from the off with both teams having chances to open the scoring inside the first few minutes.
It was the Baggies who threatened first when Jordan Pickord sent a poor clearance up instead of out.
That was latched onto by Robinson who then squared for Diangana.
But the keeper atoned for his error by making a smart low stop to keep out the winger's low drive.
Everton went straight up the other end and should have scored from a corner when Calvert-Lewin met James' delivery.
Thankfully for Albion, though, the strikers header sailed narrowly past the post.
While Bilic had been pleased with Albion for an hour against Leicester, here they were proving to be a completely different side - particularly going forward.
The Baggies were really playing well down the left where Gibbs, Diangana and Robinson were combining well.
And they deservedly opened the scoring in the tenth minute with a fabulous goal.
Pereira nipped ahead of an Everton man to produce a pass that allowed the Baggies to counter.
And Diangana, - who had collected the ball in his own-half - ran and ran and ran before lashing in a spectacular strike from 20-yards.
Albion were playing some excellent stuff and they came a whisker away from grabbing a second mid-way through the half.
Following a clever diagonal from Dara O'Shea, Furlong showed the team also carried a threat from the right by whipping in a dangerous cross.
And that was met by Jake Livermore who took a touch before firing a strike against the post.
You couldn't help but wonder if the miss would haunt the Baggies.
And so it proved when Everton got back on terms - in somewhat fortuitous circumstances - just after the half-hour mark.
Richarlison nodded the ball towards goal following a cross from the right with Calvert-Lewin back-heeling it in from what was an offside position.
The linesman raised his flag to rule the goal out.
But VAR spotted that Richarlison's header actually came off Furlong - and the goal was able to stand.
The game continued to be fairly even contest from that point.
But Albion hearts were broken on the stroke of half-time when James showed his class by finding the bottom corner with a spectacular low drive from 25-yards.
If that wasn't bad enough, though, chaos then ensued.
James made a late challenge on Gibbs who reacted by shoving the Colombian in the face.
Referee Mike Dean had no choice but to send him off. Then at half-time, Bilic was also given his matching orders for confronting the official.
Despite the drama that had unfolded, Albion got themselves back on terms shortly after the re-start.
After first winning a free-kick 25-yards out, Pereira then produced a truly stunning strike to curl the ball over the wall, back down again and into the top corner.
Within 10 minutes, though, Everton were back ahead.
A free-kick from the left was met by Richarlison with his header kept out with a smart stop from Sam Johnstone.
But it was Keane who reacted quickest with the England international then firing in from close range.
Sadly, from that point, the goals kept coming for the hosts.
Calvert-Lewin made the score 4-2 on the hour when he tapped in a cross-cum-shot from Richarlison at the back post.
The striker then grabbed his hat-trick when he powerfully headed in from a corner.
With the game out of sight, Albion made a double change with Pereira and Diangana replaced by Kyle Edwards and Matt Phillips - presumably to prevent either of them picking up an injury and making a bad day even worse.
And from that point the game was closed out by Everton comfortably, with Anchelott’s side knowing they had the points firmly in their pocket.
Everton (4-3-3): Pickford, Coleman, Keane, Mina, Digne, Doucoure (Sigurdsson 65), Allan, Gomes, Rodriguez (Kean 78), Richarlison, Calvert-Lewin (Iwobi 71).
Subs not used: Virginia, Kenny, Barnard, Davies.
Albion (3-4-3): Johnstone, O'Shea, Bartley, Ajayi, Furlong, Gibbs, Livermore, Sawyers (Field 75), Pereira (Phillips 71), Diangana (Edwards 71), Robinson.
Subs not used: Button, Kipre, Harper, Robson-Kanu.