Oldham's Matt Smith found the net in the second period to make it 3-1, but an upset was never on the cards.
So, does that mean it was a fair result? Sports Mole takes a closer look at the action.
On target 7
On target 6
Was the result fair?
Without a doubt this was a fair result. A lot of things went Everton's way, such as penalty decisions for and against in the first half, but there was an undeniable gulf in class between the two sides across the 90 minutes.
David Moyes's side played at a good tempo and performed generally well across the pitch. They defended poorly when Oldham pulled a goal back through Matt Smith, but were a cut above the League One outfit for the rest of the evening.
The Latics did not embarrass themselves by any means. Not only did they do exceptionally well to make it to this stage, they never made it comfortable for Everton. Just as the Blues looked to be coasting into the quarter-finals, they hit back through Smith to make them work for the victory.
Sports Mole's man of the match
Kevin Mirallas: Everton's wingers were the difference between the two sides this evening and this award could just as easily have gone to Seamus Coleman. Mirallas has had a tough season due to injuries, but he was on fire tonight, creating chance after chance and getting in among the goals himself.
Michael Oliver didn't exactly have his work cut out tonight. It was a relatively tame match with little need for cautions on either side. However, his decision to deny Oldham a first-half penalty when Darron Gibson appeared to handball in the area was contentious.
This is a difficult honour to hand out as both sides were generally good this evening, but Everton's dismal defending for the Oldham goal is a strong contender, as is Gibson's sitter in the 83rd minute. Nikica Jelavic set up the Irishman at point-blank range, only to watch him blast the ball into the stand.
Everton: Everton play host to Reading in the Premier League this weekend as they look to get their Champions League bid back on track.
Oldham: Oldham are in League One action against Sheffield United as they look to build on rapidly-improving league form.