The Toffees recorded a second victory on the trot to push up to seventh on the table whilst the Baggies, who have now lost three of their last four, remained 14th.
The opening goal came in the 18th minute when Leon Osman exchanged passes with Nikica Jelavic before unleashing on goal with the ball taking a deflection off Albion's Gareth McAuley and in past a wrong-footed Ben Foster.
The visitors had forced their way back into proceedings early in the second half but Everton again took control when substitute Victor Anichebe received a pass from Steven Pienaar to fire home in off the post to make it too much of a bridge to cross for the Baggies.
Pienaar could have rounded out the result with just under 15 minutes remaining when he shot Jelavic's through ball straight at Foster but in the end the two-goal cushion was enough as David Moyes' men marched along.
TRIBAL ASKS: Are Everton playing well enough at the moment to cause an upset in the FA Cup this season?
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