The Latics had failed to score away from home during their previous winless run, but Fortune's sole strike was enough to beat the division's bottom club.
Wigan manager Owen Coyle gave on-loan winger Marc Albrighton a first league start while Yeovil boss Gary Johnson restored Paddy Madden to the starting line-up following a three-game absence.
The hosts started brightly and pegged the FA Cup holders deep into their own half with a flurry of early corners, as they looked to take advantage of Wigan's gruelling 2,500-mile trip to Rubin Kazan in the Europa League on Thursday.
However Wigan and captain Emerson Boyce - making his 200th league start - held firm and should have took an early lead when Fortune raced through, but dragged his shot disappointingly wide.
Yeovil, who were looking for back-to-back wins at Huish Park, continued to shade the early exchanges with Madden at the centre of the action, firstly seeing his cute lob headed away by Ryan Shotton before firing a dipping shot narrowly over the crossbar.
But it was the Lancashire side that should have taken a slender advantage into half-time, spurning a number of glorious opportunities.
Midfielder Chris McCann hit a swirling left-footed volley wide of the post, before Albrighton's 20-yard drive rattled the crossbar.
Winger Callum McManaman also saw his close-range shot blocked on the line by on-loan Everton defender Shane Duffy, with Fortune's rebound frantically hooked away by Luke Ayling.
Wigan, looking for their first league win away from the DW Stadium since August, continued to threaten at the beginning of the second half, with the lively Albrighton skipping past his marker and finding Fortune, who headed tamely over from close range.
The Somerset side rode their luck as the Latics' pressure mounted, with Boyce heading Ben Watson's free-kick into the side-netting and Albrighton's flash shot palmed away by goalkeeper Wayne Hennessey.
Heroic defending looked like it was to thwart the visitors, with Boyce seeing his shot cleared off the line and Watson firing over.
But the visitors broke the deadlock 13 minutes from time when Fortune steered substitute Grant Holt's low cross into the empty net.