Despite dominating for the majority of the game, the closest the Toffees came to making a breakthrough was when Tim Cahill's second-half header rebounded off a post.
Neither side has been particularly prolific this season but Everton created enough chances to have put the result beyond doubt and their failure to do so will be a concern for manager David Moyes.
The result extended their winless run to seven matches and, with just three victories in the current campaign, they remain two points above the relegation zone.
Wigan, for their part, could not be criticised for hanging on at times in the hope they would get a chance to snatch victory.
It was a plan which almost worked late on when Mohamed Diame broke through only to delay his shot too long and, although the draw kept the Latics third-bottom, the character they displayed will serve them well in the expected relegation battle after Christmas.
Things did not really spark into life until after the interval, by which time the 32,853 at Goodison had endured an attritional, dogged and frustrating 45 minutes.
The improvement in quality was marginal but at least there was more action to watch.
Wigan's Ali Al Habsi was by far the busier of the two goalkeepers, palming away Steven Pienaar's long-range shot soon after the restart before clinging on to Phil Jagielka's near-post flick-on of Leighton Baines' cross.
Louis Saha's backheel inside the penalty teed up Cahill but he screwed his shot wide of the far post, sparking a manic two-minute period when Everton should have scored at least once from four attempts.
Saha has not scored in the Barclays Premier League this season and his lack of confidence appeared evident as he struggled to control Pienaar's perfect 58th-minute through-ball before poking left-footed straight at Al Habsi.
The goalkeeper had no time to reflect on that save as Cahill's header from Sylvain Distin's cross bounced back off the foot of the post, Seamus Coleman shot straight at him from close range and Pienaar fired over in quick succession.
In that short spell Everton appeared to burn themselves out as Wigan then sensed their chance to nick something from the game.
Having soaked up an enormous amount of pressure, the visitors should have punished Everton with the classic sucker punch with 20 minutes to go when Diame was put clean through after a one-two with Hugo Rodallega but he delayed long enough for Jagielka to get back with a sliding block.
In added time substitute Ronnie Stam's shot was tipped behind by Tim Howard and Rodallega headed wide the resulting corner.
Saying the second half contained the best action was not much of an endorsement of the opening 45 minutes, which began brightly for Everton but went downhill fast.
Cahill almost converted Jagielka's 60-yard pass inside the first minute but was put off by Antolin Alcaraz.
Two half-chances fell to Saha but he could not take either; the first was from Pienaar's curling cross-shot which the Frenchman could not get a touch to and the second came when he directed a far-post header wide.
In between those Marouane Fellaini had probably the best opportunity but nodded over Baines' free-kick when unmarked while Jack Rodwell could consider himself unlucky when his header deflected off Ben Watson onto the top of the net.
Wigan, to their credit, did what they had to do - which was hang on as best they could but it obviously had a negative effect on their attacking capabilities and their one real opening came when Charles N'Zogbia drilled a low cross through the six-yard box but with no team-mate near Baines hacked away.
Frustration began to grow both on and off the pitch and as the half drew to a close Hendry Thomas and Pienaar, both on yellow cards, were given their final warnings by referee Mike Oliver for persistent fouling.
They calmed down after the break as the match action livened up but neither side could ultimately do enough to earn three points.