With Hull City losing at home to Stoke City, Albion are now just three points from safety with two games remaining.
It was a win that Tony Mowbray's side thoroughly deserved against a Wigan team who crashed to their fourth defeat in their last five games.
On-loan Nancy striker Fortune headed Albion ahead into the lead after just eight minutes before Hugo Rodallega's first goal for Wigan got Steve Bruce's team back on to level terms.
But a fifth goal in five games from Chris Brunt, when he scored from the rebound after seeing his penalty saved by substitute goalkeeper Richard Kingson, and Fortune's second in the 73rd minute kept Albion dreaming of another Great Escape.
It will still be a tall order as their penultimate game of the season next Sunday is at home to Liverpool.
Albion made the perfect start when Brunt fed Gianni Zuiverloon as he cut into right-hand side of the Wigan area.
The Dutchman let fly with a fierce drive that Chris Kirland could only parry into the path of Fortune, who had the simple task of heading the ball home at the far post.
It proved to be Kirkland's final contribution to the game was he was taken off seconds later and replaced by Kingson after the England international appeared to have again succumbed to his long-running back problems.
Albion had their own goalkeeping problems before the game when Scott Carson was ruled out by a gashed hand - paving the way for veteran Dean Kiely to make his first Premier League appearance of the season.
The Republic of Ireland international was certainly not found wanting as he pulled off a stunning double save from Paul Scharner and Olivier Kapo in the 10th minute to protect Albion's advantage.
Not to be outdone, Kingson made the most of his step-up from understudy with a superb save of his own after tipping away a goalbound close-range drive from Juan Carlos Menseguez after 15 minutes.
It proved to be a pivotal moment as Wigan were level just two minutes later although Rodallega's strike had a huge slice of luck attached to it.
Rodallega was hauled down some 25 yards from goal by Zuiverloon and he got up to take the free-kick himself.
The Colombian's shot took a wicked deflection off Brunt and completely left Kiely wrong-footed as the ball squirmed away from his grasp.
If there was a slice of good fortune about Wigan's equaliser they also had to ride their luck to stay on level terms when they were once again indebted to Kingson as the Ghana international frustrated Fortune at his near post in the 41st minute.
Such was Albion's commitment to winning the game that they were always likely to be caught by a swift break and, when Antonio Valencia raced clear of Jonas Olsson on the stroke of half-time, Kiely again had to come to their rescue with another impressive save.
Kiely then denied Mario Melchiot in the 52nd minute and the value of his intervention became clear when Brunt struck.
Referee Peter Walton had no hesitation in pointing to the spot when Fortune has hauled down by Titus Bramble.
Brunt's penalty was confidently enough struck, but it caught Kingson's legs as he dived to his right.
Fortunately for Brunt, the rebound fell invitingly to him and he had the simple task of pushing the ball into an empty net from two yards with Kingson still out of position.
Albion then made the game safe when Borja Valero cut in from the right wing to roll a pass into the path of Fortune, who beat Kingson at his near post from 14 yards.