In a game of few chances the substitute struck in the dying moments to lift the Toffees above Albion after Peter Odemwingie had missed a great chance to open the scoring.
In a game of few chances Louis Saha scuffed wide for the visiting side and Peter Odemwingie blazed over when through on goal as two of the lowest scoring sides in the league struggled to make a breakthrough in the match.
But Anichebe popped up in the area after Paul Scharner failed to defend Tony Hibbert’s back post cross and the striker buried his shot past Ben Foster to seal the win which sees the Toffees go above the Baggies in the table.
Roy Hodgson was forced to make two changes to his side with Craig Dawson making his home debut after a calf injury hit the ever present Jonas Olsson and fit again James Morrison came in for Youssouf Mulumbu who was missing with a groin strain.
David Moyes was able to bring in Jack Rodwell, who had recovered from a hamstring strain and came in to replace Royston Drenthe
Neither side had been in rich scoring form with West Brom having scored just seven home goals in the league and Everton just three in its last five matches. It showed with a cagey opening as both sides passed the ball well but without penetration with a Nicky Shorey header which floated harmlessly wide the best either side could manage.
The first chance came after 20 minutes when Shane Long peeled off at the back post to meet Chris Brunt’s teasing cross but he headed over when well placed to test Tim Howard in the Everton goal.
The visiting side was patient in possession but was almost gifted the lead when Ben Foster made a hash of trying to punch Saha’s hooked cross in the area but he recovered well to block Rodwell’s follow up.
Everton was being awarded plenty of free kicks by referee Stuart Atwell and from identical positions on the left the club had chances with Saha scuffing wide when well placed inside the area and Phil Jagielka chipping over from the right after the initial Leighton Baines delivery into the area.
The Everton left back was by far his team’s most creative outlet and from another excellent whipped cross on the right Rodwell flicked a header wide as the away side ended the opening period strongly.
The second 45 minutes followed a similar pattern but the home side managed to get on the front foot and should have taken the lead right at the start but after Scharner’s header had set Odemwingie through on goal. With just Howard to beat he could only hit his shot over the bar.
The Baggies kept pushing forward and only a good challenge John Heitinga prevented Thomas from testing Howard. Brunt then shot over the bar from distance.
Moyes responded by bringing on Magaye Gueye for Rodwell and the youngster responded by immediately trying a shot from a similar distance but his went wide of the post.
The Scot followed that up with a double substitution which saw Anichebe and Denis Stracqualursi replace Phil Neville and Saha and it nearly paid dividends with Osman having his shot blocked from just outside the area by Dawson.
Scharner and Morrison both also tried their luck but neither could test Howard who was having a very easy game.
With the game seemingly drifting towards a draw, Everton struck late through Anichebe. Scharner headed Hibbert's cross back across goal for the striker to finish past Foster with several defenders attempting to block his shot.
Four minutes of added time were soon given but it was too late for West Brom, which was consigned to yet another home defeat having won just twice at the Hawthorns all season.