The Baggies started the match brightest with Gareth McAuley heading in after just nine minutes, but Kevin Mirallas equalised for the visitors on the stroke of half-time with a low drive.

Former England midfielder Barry claimed the winner in the 60th minute by nodding in from a corner. 

Moments before, West Brom goalkeeper Ben Foster had made a sublime save to deny Ramiro Funes Mori, but from the following corner delivered by Gerard Deulofeu, Mason Holgate flicked the ball on and it was steered in by Barry.

Everton registered their first win of the season after they drew their opening game 1-1 at home with Tottenham Hotspur. 

Striker Romelu Lukaku again started on the bench, before coming on for midfielder James McCarthy after just 38 minutes as Koeman changed tactics.

Tony Pulis' hosts will be disappointed to walk away empty-handed after a spirited performance that saw them take an early lead through Northern Irish centre-back McAuley, but they were on the back foot for the rest of the match as Everton pressed.

Pulis named an unchanged side to the one that beat Crystal Palace 1-0 away last weekend.

Ronald Koeman also opted to start the same team that held on for a point against Tottenham.

Koeman did have Belgium international Lukaku fit again, but opted to keep him on the bench alongside new signing Yannick Bolasie who had completed a £25 million ($32.7m) move from Crystal Palace.

Everton were unlucky not to add more goals to their tally, with Foster denying Ross Barkley and Lukaku.

Deulofeu also hit the post for the visitors in the 51st minute, before Barry scored the winner to send Everton above West Brom in the fledgling league table.

It was a first setback however for Pulis' men, who will have a chance to remedy their home form against Middlesbrough next week.