The Latics overcame a strong fightback from the Premier League outfit to earn a replay at Goodison Park thanks to an injury-time goal from the star of the fourth round
Oldham Athletic continued their FA Cup fairy tale as a last-minute strike from Matt Smith forced a fifth-round replay with Everton.
The League One side took the lead through Jordan Obita, before goals from Victor Anichebe and Phil Jagielka gave the visitors a hard-fought advantage, only for Smith to head home a corner deep into injury time to claim a 2-2 draw.
David Moyes made just two changes to the side that lost to Manchester United last weekend, with Marouane Fellaini, Steven Pienaar and Leighton Baines all involved as the Merseysiders looked to avoid the same fate as city rivals Liverpool, who were eliminated by the Latics in the last round.
The decision to name a strong side appeared set to be vindicated with Everton dominating much of the early going, although showed a distinct rustiness in the final third, with Leighton Baines' deflected free kick their best chance of the opening stages.
Everton soon made to pay for their profligacy, as they quickly fell behind with Obita slotting home from close range following a rapid counter from Lee Croft.
The home side's lead lasted less than 10 minutes, however, as Everton turned the screw before finding the leveller through Anichebe, the Nigerian powering home after Nikica Jelavic had flicked a long ball from Jagielka into his path.
Oldham were not deterred by Everton's response, and they almost re-established their advantage seconds after the equaliser, Obita again at the forefront as he saw a curling effort strike the post with Howard beaten.
The game experienced somewhat of an elongated lull after the frenetic nature of the first 25 minutes, but it was Everton who always looked the more likely to snatch the initiative - Fellaini heading over from a corner as the Belgian began to exert more influence on the encounter.
Tony Philliskirk will have been pleased to see his side go into the interval with the tie all-square, but the Premier League outfit quickly dashed his satisfaction when Jagielka rose to meet a corner from substitute Kevin Mirallas and give the visitors the lead early in the second half
The introduction of Mirallas - who came on for first-half goalscorer Anichebe - proved to be an inspired one, as he gave Everton a renewed impetus.
Oldham remained a threat despite Everton's relative dominance, and they came close to restoring parity, when Smith, the hero of the win over Liverpool, forced an excellent stop from Howard with a fierce low drive.
However, the Latics continued to struggle with the quality of the Toffees from a defensive standpoint, and Jelavic almost ended the game as a contest when he fired over following a good through-ball from Darron Gibson.