Saido Berahino's goal almost earned West Bromwich Albion a first home win of the season, but a resilient Everton fought back to steal all three points.
Berahino, who featured at the 2015 European Under-21 Championship, opened the scoring after a series of defensive errors led to West Brom winning possession in the final third before the 22-year-old broke through the middle to slide home.
It kick-started an excellent encounter which put the Midlands club in a commanding position after Craig Dawson doubled their advantage on 54 minutes.
But almost immediately from the restart the game was back on a knife edge as England midfielder Ross Barkley picked up the ball on the left, switched to the right and Gerard Deulofeu's cross was met by the head of Romelu Lukaku.
Phil Jagielka celebrates with Romelu Lukaku after he scored Everton's third goal
From then the tide was only moving in one direction and England duo Phil Jagielka and Under-19s Brendan Galloway looked solid as part of Roberto Martinez's defence.
An Arouna Kone goal in the 75th minute followed and the pressure told as Lukaku netted what turned out to be the winner with six minutes to go.
Rickie Lambert entered the fray with five minutes to go but he could do nothing to stop Everton taking all the points and moving into fifth place ahead of Sunday's Merseyside derby.
Of the 220 Premier League starters this weekend, 61 can play for England (27.7%). The 2015-16 average to date is 29.7%.
