Everton's Mr Reliable Leighton Baines was their unexpected matchwinner with two first half goals as West Brom were beaten 2-1.
The left-back smashed one in from the edge of the area before converting a penalty - his 10th success from the spot to maintain his 100% Premier League record.
Substitute Shane Long pulled a goal back midway through the second half but the Baggies, who had won just once in their previous 13 league visits, saw their recent slump extended to just one point from a possible 15.
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