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.