West Brom 0-1 Everton
Victor Anichebe scored his first league goal in 22 months as Everton snatched a late victory at West Brom.
The game was heading for a drab stalemate until Anichebe pounced on a poor header from Paul Scharner in the 87th minute to fire past Ben Foster.
The Baggies failed to register a single shot on Tim Howard's goal, Peter Odemwingie going closest with a dipping volley just over the bar.
Everton created few chances although Foster saved a Magaye Gueye volley.
They were without injured duo Jonas Olsson and Youssouf Mulumbu, with defender Craig Dawson coming in for his first start since September.
And he could hardly have had a more comfortable start in a quiet first half with both sides guilty of wayward passing.
Shane Long briefly brought the game to life in the 19th minute with a darting run behind the Everton defence, which was spotted by Chris Brunt. The winger delivered a pinpoint cross but the striker's header looped over the bar.
Foster presented Everton with their first sight of goal five minutes later when his weak punch from Louis Saha's cross dropped to the feet of fit-again Jack Rodwell, but the Baggies keeper was able to scramble a block on his shot.
Saha then screwed a half-volley horribly wide before the half petered out in a miserable opening to the New Year.
West Brom looked to up the tempo after the restart and almost surprised the Toffees in the opening minutes.
Brunt's hopeful header forward set Odemwingie free but the striker's drive flashed over the bar with just Howard to beat.
Odemwingie and Brunt then shot just off-target as they pushed the visitors back.
Everton boss David Moyes responded by bringing on forwards Anichebe, Gueye and Denis Stracqualursi as his side went in search of the three points.
Gueye hit a crisp near-post volley that was well held by Foster and Stracqualursi wasted a good opportunity after neatly dribbling into the box before Anichebe struck the killer blow with three minutes to go.
Scharner lost his bearings from a Tony Hibbert cross and could only head the ball down in his own six-yard box, where Anichebe controlled it before swivelling and blasting the ball into the net.
Manager Roy Hodgson could not hide his frustration in the dugout as Everton leapfrogged his side into the top half of the Premier League at the final whistle.
Everton manager David Moyes: "We tried to make it difficult for West Brom like they make it difficult for teams. It was a bit of a stalemate at times. I don't think you'll buy the DVD of the game.
"But at the end of the day, this has been a hard place for us. We've not won here for a while and the victory gives us a chance to look forward.
"(Victor Anichebe) has missed a lot of football. At times he lacks a bit of self-confidence but the goal today and the reaction of the supporters will help him."
West Brom manager Roy Hodgson: "I'm very disappointed we couldn't continue what has been a very good run in the last three games and continue playing the same level of football.
"Today we've given three very big points to our rivals. They did well enough to deserve a draw but must be feeling very grateful that we gifted them a goal three minutes from time.
"I don't think we created that many chances. I don't think it was as good a performance attacking-wise."