It had initially seemed an even bigger shock was on the cards as the hosts took a 13th-minute lead through Jordan Obita.
However, Everton responded 11 minutes later, through Victor Anichebe, and went on to take the lead thanks to Phil Jagielka's header moments after halftime.
Despite the Toffees dominating large parts of the second period, Smith's last-gasp heroics ensured Oldham remain in the competition and travel to Goodison Park for a money-spinning replay.
Here are six Everton-related talking points to stem from this fixture.
Before any action is analysed, it's important to note David Moyes' continuing respect and desire towards the FA Cup.
Much has been written in the last few days about the precarious state of his contract, but, once again, Moyes showed his fierce ambition to win Everton some silverware by fielding his strongest side possible.
The likes of Leon Osman, Phil Jagielka and Leighton Baines all racked up their 30th game of the season, and there was certainly no temptation to rotate as so many other sides have done.
The fact the Toffees' roster is so thin compared to their rivals may hurt them in the long run, yet it seems Moyes doesn't want any regrets over selection between now and the end of the season.
As desperate as he is to make the Champions League with Everton, he's clearly not going to jeopardise his side's chances of hoisting a cup this season—which remains an equal priority.
As has become a recurrent theme in the Premier League this season, Everton finished the game regretting a number of missed opportunities in front of goal.
Having taken the lead through Jagielka's header, the Toffees proceeded to dominate second-half proceedings without ever finishing the job.
Nikica Jelavic and Leon Osman missed two particularly inviting openings, and David Moyes watched his side spurn several other half-chances before Oldham roused themselves for a predictable late onslaught.
With just a fragile lead to cling on to, Everton's box was suddenly overloaded, and it wasn't entirely surprising when Smith bundled home an equaliser.
As has been their tendency all season, the Toffees were unable to ever find that vital two-goal cushion which would have prevented any of this game's last-gasp drama.
While on the field, Victor Anichebe was once again a key performer for his side, registering his seventh goal of the season.
He's now scored the same amount as Nikica Jelavic—in nine fewer outings—and also has two more assists to his name than the Croatian.
Featuring in his 20th game of the season, a milestone he hasn't reached since 2009, the Nigerian continued on with what's been a hugely impressive individual campaign.
His pace and power concerned Oldham throughout the first half and with every passing game he's becoming an increasingly important weapon for David Moyes.
Sadly, as has all-too-often been the case during his career, injury prevented him from returning for the second half and his side clearly missed his physicality.
With Jelavic continuing to misfire in front of goal, Moyes will be anxious for Anichebe to make a speedy recovery.
Everton finished last season with more different scorers than any other side in the Premier League.
Having such a variety of threats is clearly a handy trait to bring and the Toffees seem keen to continue the trend in this year's FA Cup.
After strikes from Jagielka and Anichebe, Everton have now scored nine goals from nine different players in this season's competition.
Jagielka's finish was an especially timely boost with the Toffees struggling to find goals from their centre-backs all year.
According to EPL Index, John Heitinga, Sylvain Distin and Jagielka have missed 10 out of 10 clear-cut chances in the Premier League, with Jagielka's strike against Wigan the only goal between the trio.
Strangely, all three defenders have now registered in cup competition and Moyes will hope this finish can spark some much needed final-third contributions from his centre-backs.
Whisper it quietly but in the last few weeks Tim Howard has slowly began resembling his familiar old self in Everton's goal.
By his own high standards the American's endured an inconsistent season, yet his contribution against Manchester United, and again here at Oldham, were far more typical of his Everton career.
As defenders dawdled he was inspired during Oldham's late rally, pulling off a pair of stunning reflex saves that should have seen his side progress.
Matt Smith's last-gasp effort will deflect the attention away from Howard but he's certainly shown more encouraging signs during the past few games.
As frustrating as it is to concede so late in a game, Everton must recognise the enticing opportunity that remains on the horizon.
Arsenal's shock exit earlier in the day further reduced the number Premier League heavyweights remaining in the FA Cup. With a favourable tie in Sunday's draw, the Toffees will be tantalisingly close to another trip to Wembley.
Given the amount of surprising results in this year's competition, it certainly could have been significantly worse at Oldham, as Liverpool found out in the previous round.
Regardless of the inconvenience of facing a replay, the most important outcome is that Everton remain represented in Sunday's draw and still within reach of Wembley.