ALBION'S travails at home spilt over into 2012 as sub Victor Anichebe grabbed a late winner for the Toffees.
In a match bereft of clear-cut openings, Peter Odemwingie wasted the best chance of the fixture when he blazed over from just inside the box at the start of the second half.
The first Barclays Premier League fixture of the New Year appeared to be petering out into a goalless draw until Anichebe sentenced the Baggies to their sixth home defeat of the season in the 87th minute.
The two teams were separated by just a place and a point before kick-off as 11th entertained 12th.
Craig Dawson was handed a surprise Barclays Premier League home debut as Jonas Olsson's ever-present league record was ended by a calf injury. James Morrison made a timely return to fitness, replacing groin-injury victim Youssouf Mulumbu in central midfield.
David Moyes made one change, with Jack Rodwell coming in for Roysten Drenthe.
Despite the previous night's New Year celebrations and the early kick-off, the home fans turned up determined to get right behind the team and a flowing move had them on their feet in the fourth minute. Chris Brunt fed Jerome Thomas who saw his right-wing cross headed wide by Nicky Shorey at the back post.
Albion had started the game brightly, with Thomas looking lively down the right, but they got little change out of a well-drilled Everton backline during what proved error-strewn early exchanges.
It was a little out of the blue, but the game's first real chance arrived in the 18th minute - and it came the Baggies' way.
Brunt curled a terrific ball into the box and the slightly off-balance Shane Long headed just over from ten yards.
Two blocked shots by John Heitinga and Rodwell, both from well from outside the box, is all Everton had managed to muster as the half passed its midpoint.
However, Albion did have a moment of concern on 24 when Ben Foster punched Louis Saha's centre straight to Rodwell after the hosts had only partially dealt with a Leon Osman corner. The Albion No.1 redeemed himself by deflecting over Rodwell's goalbound effort.
The Toffees gradually began to put the Baggies backline under pressure and it was a case of all hands to the pump to deal with a couple of wicked Leighton Baines corners.
It was from another Baines set-piece that Everton created their best chance on 33. The visitors worked the ball back to Saha who scuffed his half-volley harmlessly wide from 12 yards.
Two minutes later, yet another Baines centre - from another free-kick - eventually fell to Phil Jagielka in the Baggies' box, but the England centre-half sent a looping shot well wide.
Albion were struggling to get out of their own half and Rodwell was the next to threaten, heading wide from a Baines corner.
But the Baggies steadily improved as the half drew to a close and Sylvain Distin had to pull off a wonderful last-ditch challenge in the box to deny Thomas a clear run at goal.
Hodgson's men should have been a goal to the good less than two minutes after the restart.
Morrison headed Odemwingie clean through but, with just Tim Howard to beat, last season's top scorer blazed the bouncing ball over from just inside the area.
However, the Albion striker was beginning to look dangerous and Heitinga did well to divert the Nigerian's shot wide after he had burst into the Everton box.
The Baggies were slowly getting on top but Brunt was well off target with an ambitious 25-yard drive.
Both teams struggled to create further chances and Saha failed to trouble Foster's goal with a long-range grass-cutter on 58.
Back came Albion and Jagielka did well to block Brunt's goalbound shot from Morrison's lofted pass.
Moments later, Howard rushed off his line to prevent Long getting on the end of Thomas' centre.
The game was slowly coming to life and Tim Cahill saw a header from Tony Hibbert's centre clip an Albion defender and loop straight to Foster.
The efforts at goal were now coming more readily and Paul Scharner hit a 25-yarder just over.
Foster was called on to make his first awkward save of the game on 68 and he was up to the task, clutching sub Magaye Gueye's fierce shot at his near post after Osman's forceful run.
After a lull in the action, Morrison smashed a 20-yard volley well over from Heitinga's headed clearance.
Dawson had looked comfortable on what was only his second top-flight appearance and he did well to prevent Osman getting on the end of Anichebe's cross nine minutes from time.
But just as the game appeared to be petering out, disaster struck in the 87th minute.
Osman played in Hibbert down the right and Scharner, in attempting to clear the cross, inadvertently headed the ball back into the goalmouth and Anichebe hooked home from close range.
It was a bitter pill for the Baggies to swallow having rarely looked in danger throughout the game.
However, they had also failed to seriously test Howard and that remained the case until referee Stuart Attwell blew up for full-time.
ALBION (4-4-2): Foster; Jones, McAuley, Dawson, Shorey; Thomas, Scharner, Morrison, Brunt (c) (Dorrans 90+3); Long, Odemwingie. Subs not used: Fulop (gk), Thorne, Tchoyi, Fortune, Jara Reyes, Cox.
EVERTON (4-4-1-1): Howard; Hibbert, Distin, Jagielka, Baines; Osman, Heitinga, Neville (c) (Anichebe 65), Rodwell (Gueye 57); Cahill; Saha (Stracqualursi 65). Subs not used: Mucha (gk), Bilyaletdinov, McFadden, Barkley.
GOALS: EVERTON - Anichebe (87).
BOOKINGS: EVERTON - Baines (foul 85), Stracqualursi (foul 90+3).
REFEREE: S Attwell (Warwickshire).
ALBION STARMAN: James Morrison.