It was by no means an impressive and pretty display by Carlo Ancelotti's side as the Baggies were the better side but they took their chance when it came to them and that was enough to see them seal three points.
In fact, the hosts were sure that their efforts secured them a point when Mbaye Diagne curled the ball into the back of the net, but the goal was chalked out for offside.
For West Brom after coming away with nothing their chances of survival now are slim, to say the least as with 11 games remaining they sit nine points away from safety.
Story of the game
The Baggies made a great start to the clash and were nearly ahead after two minutes when Conor Gallagher's cross from the right found Diagne unmarked and his header from close range looked to be destined for the left-hand corner.
However, Jordan Pickford came scrambling across his goal to claw the ball to safety.
The home side went on to build on from that early chance as in the opening stages there was no doubt that they were the brighter out of the two teams with Diagne having another effort on goal inside 17 minutes, but this time he could only blaze the ball over the crossbar.
Three minutes later, Matt Phillips cut in from the left but his low shot was cleared away by Ben Godfrey before it was able to reach Pickford's goal.
Then seven minutes before the break, with the game's tempo beginning to dye down, the visitors had their first sign of goal when Dominic Calvert-Lewin slipped in Richarlison down the left.
However, Darnell Furlong did brilliantly to come across and make a goal-saving block as the ball looped on to the roof of the net.
A few minutes later the best chance of the half came and it fell to Carlo Ancelotti's side when, via a deflection off Kyle Bartley, the ball found it's way through to Calvert-Lewin, who was now one on one with Sam Johnstone, but his low shot was saved by the legs of the West Brom number one.
After the break, Sam Allardyce's side continued the way in which they played in the first period but they just lacked that finishing touch as Matheus Pereira had an effort from range which was comfortably gathered by Pickford.
Two minutes later though the hosts should have been ahead and it was Diagne again as he got on the end of Bartley's flicked on header, but from point-blank range, he could not direct his header on target.
A few moments later Gallagher showed to have quick and smart feet inside the area but his low drive flashed across the face of goal as it just was not quite falling for West Brom.
Then with 25 minutes remaining, the home side rued missing their earlier opportunities as the Toffees broke the deadlock.
A cross from the left-hand side by Gylfi Sigurdsson, who had only just entered the field, landed onto the head of Richarlison, who got there ahead of Johnstone and he managed to power the ball home.
After the opener, Everton for the first time really in the game began to get a foothold and could have doubled their advantage but Calvert-Lewin slicked the ball over the bar after being found by a Lucas Digne cutback.
With Everton looking to see out the win, in the dying embers Diagne though he rescued a point for West Brom when he brought down Furlong's cross and guided the ball into the back of the net, but the flag went up for offside which in turn broke the host's hearts.
Baggies failure to provide the finishing touch costs them again
Up until the goal, West Brom’s performance could not really be criticised. Against a very good Everton side, they outplayed them for a large proportion of the match.
However, when your down towards the back end of the table and when you come up against a team of the quality that the Toffees possess, if you do not take your chances you are ultimately going to get punished and that is exactly what happened
Diagne was the culprit for the majority of their missed opportunities,s but throughout the entirety of the game, he looked like a threat and it can be seen that the decision to rule out his late strike as harsh.
Despite him not being able to find the finishing touch this time around, he did provide the Baggies with a focal point going forward- something that in truth that they have been lacking all season.
However, it could prove to be a little bit too little, too late as their struggle to score on a regular basis this season is one of the main factors that will cost them a place in the league for next season which at the moment seems the likely scenario.
Toffees love playing at the Hawthorns
While for Everton, this result marks six games since they last lost at the Hawthorns, a run which stretches back to September 2012 when they were managed by the current West Ham United manager David Moyes.
It also means that Ancelotti's side now have only lost once in 13 games against the Baggies with their last defeat against tonight’s opponents coming in February 2016.
Not only does tonight’s win continue the club’s good form against West Brom, it means that Everton have now won nine games on the road which equals their best away record in the Premier League era with them achieving the same amount during the 2008/09 campaign.
This in itself shows a change of fortunes for the club, and not just this season, but potentially for campaign's going forward under Ancelotti and the crop of players that he currently has under his ranks.
Star man- André Gomes
The midfielder who has started Everton’s last three games looked very comfortable and composed in midfield at the Hawthorns.
He rarely conceded possession of the ball and even through the periods that the Toffees were struggling in during the game, he was someone that continued to be consistent and that Ancelotti could always rely on.
The former Barcelona player has been a consistent force in Everton’s midfield so far this season as has featured in 20 of the 26 league games.