The 6ft 6in striker, who produced an all-action display to score twice in Latics' round four triumph over Liverpool, was at it again with a towering header deep in stoppage time having stepped off the bench just after the hour mark.
Jordan Obita gave the League One strugglers the lead but the 2009 FA Cup runners-up and last season's semi-finalists struck back thanks to goals from Victor Anichebe and Phil Jagielka before Smith's late intervention.
The home side started on the front foot and stunned their opponents by taking the lead after 13 minutes. Lee Croft made the initial break down the right after a poor challenge by Leon Osman before his low measured ball into the box was slotted into the back of the net by on-loan Reading midfielder Obita.
However, Everton struck back 11 minutes later as Anichebe cleverly collected Nikica Jelavic's knock down by nudging Jean Yves Mvoto off the ball and smashing his shot beyond Dean Bouzanis.
Moments later, the Latics came close to restoring their lead when the lively Obita saw his effort narrowly tipped on to the far post by Tim Howard.
The Toffees went ahead three minutes after the interval thanks to a rare goal from Jagielka. Kevin Mirallas' corner kick was headed home from close range by the England defender after some poor defending by Lee Barnard and a woeful attempt at a punch by goalkeeper Bouzanis.
Everton were intent on driving home their advantage and some deft interplay between Steven Pienaar and Marouane Fellaini saw the former bring Bouzanis into the action once more.
Another Mirallas corner had Oldham in trouble before the hour, arching past the massed ranks at the near post and narrowly evading Leon Osman.
Caretaker manager Tony Philliskirk then sent on the 23-year-old Manchester University business management graduate Smith onto the field.
In the 89th minute Robbie Simpson had a glorious chance to earn a replay as he shrugged off the attentions of Phil Neville to collect James Tarkowski's wonderfully-weighted lofted pass, but Howard stopped a shot that lacked purchase before seeing the rebound lashed into the side netting.
However, Smith had the last laugh as he sent the home fans into ecstasy after climbing above his own goalkeeper in the visitors' box to head Jonathan Grounds' corner in the fourth and final frantic minute of stoppage time.