Having been forced into a replay, the Toffees were far more authoritative the second time around, and—although Oldham never gave in—the hosts were relatively comfortable throughout.
Kevin Mirallas opened the scoring with 15 minutes on the clock, prodding home a sumptuous cross from Darron Gibson.
After a pair of debatable penalty shouts for either side, Everton were awarded a spot-kick on 34 minutes, which Leighton Baines duly converted.
Just after the hour mark, Leon Osman glanced in a third for the Toffees before Matt Smith powered home a consolation that kept the tie competitive.
Here are six Everton-related talking points to emerge from this fixture.