Matt Smith continued his goalscoring record in the competition but the English Premier League team proved too strong for Oldham's fairytale adventure in the cup to continue further.
FA Cup: Everton end battling Oldham's hopes with 3-1 replay victory
Everton booked their place in the quarter-finals of the FA Cup and ended Oldham's memorable run with a routine 3-1 replay victory at Goodison Park.
The English Premier League side put their opponents under pressure from the opening minutes in a bid to avoid repeating the nerves of the first match.
Kevin Mirallas and a Leighton Baines penalty put Everton two goals up before half time, with Leon Osman adding a third in the second half before Matt Smith's consolation strike.
The result gave the Merseyside team their first win of February at the fifth and final time of asking, but afterwards Steve Round, the Everton assistant coach, was quick to pay tribute to their opponents.
"It was a tough game," he said. "I thought Oldham put a right shift in and pushed us all the way.
"They were a credit to the manager and to themselves. I thought they really acquitted themselves right and made it very tough.
"Having said that, I think we matched them for the attitude and then your quality comes through at the end.
"You saw that with one or two of the goals that we scored and unfortunately we missed a couple of chances to maybe make it a bit more clear-cut."
Oldham looked to use the pace of left-winger Jordan Obita in the early stages, but a pair of attempted through balls from Jose Baxter were misplaced when trying to send clear the man who opened the scoring in the first game. That honour on this occasion went to Mirallas, who applied the finish to Gibson's superb cross from the right.
Oldham were almost back on terms immediately as Baxter collected Lee Barnard's lay off to launch an exquisite lofted effort over Everton goalkeeper Tim Howard from 25 yards and against the upright.
Referee Michael Oliver was disinterested in a 24th-minute penalty shout for the hosts, despite replays suggesting Latics centre-back James Tarkowski had a good handful of Nikica Jelavic's shirt as he battled to meet Phil Neville's cross. Baines then scythed an effort from distance that Dean Bouzanis in the Oldham goal did superbly well to keep out of the bottom corner.
Tarkowski again engaged in an unseemly grapple with Jelavic as Seamus Coleman delivered from the right by-line but, although Oliver missed that indiscretion, the referee pointed to the spot when the cross struck fullback Brown's outstretched arm. Bouzanis got a hand to Baines' 34th-minute penalty but there was sufficient power for the ball to slip underneath him and into the net.
In the 55th minute, Latics introduced Smith in place of the ineffective Chris Iwelumo, but Everton responded by extending their lead slightly fortuitously in the 62nd minute.
Steven Pienaar's in-swinging ball from the left was glanced goalwards by Osman, a header that evaded both Jelavic's outstretched boot and Bouzanis' fumbling attempts to gather.
This time Oldham did find a quick response through an increasingly familiar source - Smith allowed far too much space to power home Jonathan Grounds' corner. Smith then headed towards goal as the curtain fell in Oldham's cup exploits but Howard would not be beaten again.
Afterwards Tony Philliskirk, the Oldham caretaker manager, admitted he felt little but pride in the way his side had performed.
"When we went 3-0 down it would have been very easy for people to be thinking it was going to be four or five but I thought we responded magnificently in the second half.
"Ironically, when they scored the third goal we were probably having our best spell in the game.
"It was disappointing to concede that third but the lads kept going, Matt's got another great goal and I thought we played some smashing stuff in the second half.
"You never know, if we'd got another one it would have been an interesting end to the game."
Everton will now face Wigan Athletic at Goodison Park in the sixth round of the FA Cup.
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