Roberto Martinez opted for a 4-4-2 formation and his side was tested defensively from the early stages as Everton set a frantic tempo, attacking the visiting goal early on down the left-hand side.
The left wing was to prove a problem throughout the encounter, with Leighton Baines and Steven Pienaar linking up well to trouble the Wigan defence on numerous occasions.
Despite Everton's early dominance, the visiting defence held out throughout the first half, with Everton unable to capitalise on the myriad set-pieces which they were presented with.
The best chances of the first half came from a Tim Cahill cross just after the half-hour mark.
The Australian drove the ball hard and low across the Wigan goal towards the outstretched leg of Louis Saha, who had only a fraction of a second to direct his shot inches over the crossbar into the Everton fans behind.
Everton began the second half brightly and Wigan were put under pressure early on after Tony Hibbert's cross found Cahill in space only for Saha to be denied by Mike Pollitt.
Despite the continued Everton pressure, a lapse in concentration from Hibbert allowed Wigan to break the deadlock through Paul Scharner, who found himself completely unmarked at the back-post from a Charles N'Zogbia cross.
Hibbert looked bemused but in truth the error was his, much to the frustration of manager David Moyes on the touchline.
However, the lead was shortlived as the home side drew level six minutes later courtesy of a well-placed Saha header.
The Frenchman rose well to connect with a Baines corner and directed the ball straight into the ground to leave the Wigan keeper stranded.
With just over ten minutes remaining, Jo replaced Saha in Everton's attack and immediately came close to finding a winner when Marouane Fellaini's through-ball allowed him time within the box, but his low shot was superbly saved by Pollitt.
Everton's winner came from a penalty deep into stoppage time after Jo was brought down by Emmerson Boyce as he stormed into the box.
The referee had little option but to point to the spot and Baines directed a solid strike into the roof of the net to grab a late winner.