The powerful midfielder bundled home less than a minute after the break after a Nigel Martyn fumble in a superbly contested encounter at Goodison Park.
In the face of a terrible start to the campaign at home and abroad Goodison boss David Moyes approached a must-win clash with a must-not-lose line-up, opting for a cautious one-up-front system headed by midfielder James McFadden. Tim Cahill continued in midfield despite a tired start to the campaign, with Lee Carsley and James Beattie on the injured list.
Wigan boss Paul Jewell knew a win would take his highflying Premiership newcomers and awarded Henri Camara a start in attack following his goalscoring substitute appearance against Middlesbrough last weekend.
As if handed the initiative by the home side's selection, The Latics started the brighter. Jason Roberts outpaced Joeph Yobo, before Jimmy Bullard fired just over from 30 yards.
Simon Davies was booked for two early midfield lunges as Wigan stifled the Blues' attempts to get men forward from midfield.
But the jaded Toffees still proved a sticky proposition with a beautifully floated header from Kevin Kilbane clipping the decidedly unsure John Filan's crossbar. At the other end, Nuno Valente cleared off the line from a bullet header from Pascal Chimbonda.
A pair of fine blocks from former Liverpool stopper Stephane Henchoz midway through the half kept the scores even, before Davies curled a 45-yard effort just over the bar. As both sides reaffirmed their desire to leave the game with maximum points, it was end-to-end stuff, but Everton were noticeably gaining confidence and, in turn, the ascendancy.
But Wigan, again on the break, came back strongly, as a brilliant cross from Chimbonda was anxiously turned behind by Phil Neville with Roberts lurking at the back post.
Confusion reigned in the Blues defence Martyn drove his boot into the face of his own defender Yobo as Camara tried to sneak in behind the Everton backline as the sides went in level at half-time.
It didn't stay that way for long as Wigan took the lead within a minute of the restart through Francis. Roberts pulled the ball back for Camara whose shot was spilled by Martin and bundled home by Francis.
Everton were shell-shocked and staring a fifth Premiership defeat in six games directly in the face. The crowd were agitated, the players nervous and Wigan, buoyed by a boisterous travelling army looked to press home their advantage.
They should have on 58 minutes when Roberts again pulled the ball back from Camara whose shot was cleared off the line by Neville.
Things warmed up for the home side when Marcus Bent was brought on to give them long-overdue presence up-front as Everton searched for the elusive leveller.
It almost came 20 minutes from time as a driven shot across goal beat Filan, the post and Bent's despairing lunge.
Bent had the ball in the net with 12 minutes to go, but Cahill was harshly adjudged to have impeded a Wigan defender before Bent bundled the ball home.
Filan then pulled off a wonderful save from Bent's flick as Wigan clung on for their lives.
Predictably, boos echoed around Goodison Park as the team who scaled the heights of fourth place last term remain rooted in the bottom three.
Man of the Match: Pascal Chimbonda - Was at the heart of a superb Latics defence that held on to make sure of another valuable victory.