Smith produced an all-action display to score twice in Latics' round four triumph over Liverpool, but had been sidelined since with a shoulder injury sustained in the match.
But the 23-year-old Manchester University business management graduate, who Oldham plucked from non-league obscurity at Solihull Moors, climbed off the bench to head home Jonathan Grounds' corner in the fourth and final frantic minute of stoppage time.
As was the case against Liverpool, Latics - playing under caretaker manager Tony Philliskirk - had their Merseyside opponents reeling when on-loan Reading winger Jordan Obita gave them a 13th-minute lead.
Goals from Victor Anichebe and Phil Jagielka either side of half-time put David Moyes' men in the driving seat but Everton goalkeeper Tim Howard was forced to save well from Smith and Robbie Simpson.
Howard was finally beaten as Smith prospered in a crowded penalty area that featured Latics keeper Dean Bouzanis attacking Grounds' decisive delivery.
Lee Croft broke unchallenged from his own half down the Everton left before driving low across goal where Obita's perfectly-timed run was rewarded with a tap-in for the opener.
The lead remained intact for 11 minutes until Everton successfully took a direct rout to goal. Jagielka's raking long ball was flicked on by Jelavic and Anichebe got the better of Jean-Yves Mvoto to rifle past Bouzanis.
Jelavic had a new partner in attack for the second period as Mirallas replaced hamstring victim Anichebe and the new man would make an instant impact in the 48th minute when his in-swinging corner from the left caught out Bouzanis, allowing Jagielka to steal in front and nod into an unguarded net.
In the 89th minute Simpson had a glorious chance to earn a replay as he shrugged off the attentions of Phil Neville to collect Tarkowski's wonderfully-weighted lofted pass, but Howard stopped the shot before seeing the rebound lashed into the side netting before Smith, much to Simpson's relief and the locals' delight, sensationally spared his blushes.
