The Toffees forward netted a second-half hat-trick at the Stadium of Light, largely down to substitutions made by the Dutch manager.
The Belgian forward had previously gone on a run of 13 games without scoring for his club, then like London buses they all came at once.
After a flat first half, Everton took hold of the game, racing into the three-goal lead in a frantic 11 minutes.
Gerard Deulofeu came off the bench at half-time, proving to be a nuisance to David Moyes’ side.
But it was Koeman and Lukaku who made the headlines as Everton move to third in the Premier League table.
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