Toffees youngster Anthony Gordon scored the only goal of the game midway through the first half, when his deflected shot burst past David De Gea.
United enjoyed long spells of pressure and possession in both halves, but struggled to eke out a really clear chance for much of the 90 minutes.
Cristiano Ronaldo's late, late snapshot could have earned us a point, but England goalkeeper Jordan Pickford did well to repel the sharp effort.
FIRST HALF – A BATTLE OF NERVES
Before this game had even kicked off, you could sense the importance of this fixture around Goodison Park.