Fortune's goal came 15 minutes from time from a Latics counter-attack. He cut inside Tony Diagne and fired a thunderous right-foot shot from just outside the area past goalkeeper Barry Roche's outstretched left hand.
Summer signing Grant Holt should have put the FA Cup holders ahead early on but lifted his shot wide when one-on-one with Roche, who soon had to deny Wigan skipper Emmerson Boyce.
Callum McManaman and Boyce once more went close at the end of the first half after Ryan Williams had forced Scott Carson to tip a 20-yard free-kick over the crossbar at the other end.
Williams tested Carson with another set piece after the break before Fortune's strike settled the game.