Latics two down at the break
Goals from Kevin Miralles and Leighton Baines gave Everton a 2-0 half-time lead in the fifth-round replay at Goodison Park.
Baines failed to find his range firing the free kick into the defensive wall.
It was the only moment of danger as Latics more than matched their Premier League opponents in the opening stages.
However, the breakthrough came from Everton after quarter of an hour.
Darron Gibson crossed from the right and Miralles stole in at the near post to fire low past keeper Dean Bouzanis from seven yards.
Latics were desperately unlucky not to equalise within two minutes when Lee Barnard set up Jose Baxter (pictured) who curled a shot from the edge of the box past Tim Howard only to see it strike the upright to the left of the keeper.
Bouzanis prevented Everton from adding a second goal just short of the half hour when he pulled off a superb save to turn a 30-yard drive from Baines round the post for a corner.
Everton doubled their lead in the 34th minute after Connor Brown conceded a penalty for handball following a right-wing cross from Seamus Coleman.
Baines scored from the spot, but only just managed to squueze the ball low to the left of Bouzanis who got a hand to the ball.
Half-time: Everton 2, Latics 0.