The Toffees had made a brilliant start to their campaign with two impressive victories but were put back in their place as the Baggies moved to third position with their seventh point as they continue their unbeaten beginning to the new campaign.
West Brom edged ahead in the 65th minute when Shane Long knocked it home from close range after getting on the end of Peter Odemwingie's firm low cross from the left before Gareth McAuley added a second eight minutes from time with a flicked close range from Chris Brunt's inswinging cross.
The Everton gloveman has a lot more to do than his Albion counterpart Ben Foster who was required to make just one save whilst Howard was on hand a number of times to keep David Moyes'men in the contest.
Marouane Fellaini had a great chance to put the Toffees ahead in the 64th minute when he was found in space in the area but he ballooned his fundamental left-footed effort over the crossbar, not even forcing Foster into a save.
That proved costly as Albion hit the lead not long after and did not look back as their impressive start to the season rolls along. Everton will now head back to the drawing board after suffering a loss but they will be looking to take any positives out of the fixture so they can build on what they achieved in the opening two matches.
The Hawthorns, West Bromwich - 25,383