Shane Long came off the bench to halve the deficit in the second half as the visiting Baggies went in search of an equalising goal that ultimately never materialised.
Below, Sports Mole has looked back over the 90 minutes to determine if West Brom can argue that they deserved a draw for their efforts.
On target 4
On target 4
Was the result fair?
A 2-1 scoreline often looks a nervy one and at times this was a close encounter. However, during the first half these two teams looked worlds apart. West Brom improved in the second half, but not enough to argue that they deserved to leave Goodison with a share of the spoils.
The Toffees will not have played many better halves than the one that they produced during the opening 45 minutes here. Their passing was slick and they got the goals that the display warranted. Even in the second half when they came under more pressure, they still looked dangerous on the counter and defended extremely well.
West Brom's performance
The saying 'it's a game of two halves' would sum West Brom's display tonight up nicely. During the first 45 minutes they barely had a shot and were wasteful in possession. However, after the restart they looked a different side - one that put pressure on Everton and forced mistakes that weren't coming prior to that. Steve Clarke is beyond to be left wondering 'what if?'
Sports Mole's man of the match
Leighton Baines: A full-back that scores twice cannot be ignored, and that's why Baines takes the award. Not just for his goals though, because he got forward well all night in support of Steven Pienaar and when he was required to defend, he did so with minimal fuss.
Jonny Heitinga: hang your head in shame, young man! He did well to get back on the line to stop Romelu Lukaku from scoring for West Brom, but his touch simply popped up into the air for a grateful Long to nod into an empty net.
A very quiet evening for Michael Oliver, who only got the yellow card out when it was necessary. The one major decision centred around giving Everton a penalty, which Oliver got spot on. Claudio Yacob clearly hauled down Victor Anichebe inside the area.
Everton: The Toffees remain at Goodison Park this coming Saturday when struggling Aston Villa make the trip to Merseyside.
West Brom: A day later West Brom are also at home, as they play host to Tottenham Hotspur.