Baggies' top scorer Solomon Rondon struck home from close range in the 14th minute after Jonas Olsson's flick on.Everton manager Roberto Martinez will be left wondering just how his midtable team failed to score given its almost total dominance of possession.
West Brom's first league win in six matches moved the club eight points above the relegation zone.
Related story
Everton beats West Brom 2-1
