Tuncay's header was the Turkish striker's fifth goal of the season
Tuncay's well-taken header denied Wigan a much-needed victory and kept up Stoke's unbeaten start to 2010.
Paul Scharner's spectacular first-half header from just inside the box looked to have put Wigan on course for a win.
And Hugo Rodallega went close to extending the lead with an overhead kick which clipped the crossbar.
But Stoke drew level through Tuncay's header from Matthew Etherington's cross before Mamady Sidibe and James Beattie missed chances to win the game.
Stoke manager Tony Pulis will be the happier with a rare away point which stretched his side's unbeaten run to seven games.
Roberto Martinez's Wigan appear destined for a battle to avoid the drop after picking up just seven points from their last 10 games and fans will be disappointed to see the team surrender a lead once again.
Wigan have now lost 16 points from winning positions, which alongside Bolton is the joint worst record in the league.
Pulis dropped Ricardo Fuller to the bench following his arrest over a nightclub incident at the weekend, while Martinez restored Jason Scotland alongside Rodallega.
Wigan attitude pleases Martinez
Despite the Stoke fans making more noise than their counterparts, Wigan made the brighter start, with Rodallega and Charles N'Zogbia stretching the visitors' defence.
The opening goal came courtesy of a free-kick after Etherington's body check on N'Zogbia. The delivery found Scharner, who leapt, and from fully 16 yards, headed the ball past Thomas Sorensen's outstretched left hand.
N'Zogbia continued to look the most skilful player on the pitch, troubling Stoke with several pacy runs.
But Stoke improved as the half wore on and went close when Robert Huth's free kick found its way through to Ryan Shawcross and the centre-half's shot on the turn was blocked by two Wigan defenders.
Pulis pleased to extend Stoke run
Moments later Stoke forward Sidibe was granted the time and space to line up a volley on the edge of the area, but he sliced his effort horribly wide.
Stoke had a great chance to equalise early in the second half when a deep free-kick found Robert Huth at the far post. The tall defender headed the ball into Tuncay's path but the Turkish striker failed to make a clean contact four yards out.
Pulis sent on Fuller for Rory Delap as Stoke went in search of an equaliser, while Martinez brought on Jordi Gomez for Scotland in an attempt to shore things up.
Although Wigan seemed content to soak up pressure from the visitors, they went close to doubling their lead on the counter-attack.
Rodallega controlled a long ball superbly and teed himself up for an overhead kick, which clipped the top of the bar.
Shortly afterwards, Sidibe found space in the area but his shot was well saved by Chris Kirkland.
But the Wigan goalkeeper could do nothing to prevent Stoke drawing level in the 74th minute.
Fuller broke clear down the right and his low cross was cleared as far as Etherington. The winger manoeuvred the ball onto his left foot and delivered a cross for an unmarked Tuncay to head in.
Two minutes later, the Potters almost turned the game around as Fuller nodded Etherington's cross back for Sidibe, who saw his header bounce off the crossbar.
And with seconds on the clock, England hopeful Etherington pulled the ball back to Beattie in space on the edge of the box. The former England striker's shot was sweetly struck but Kirkland, at full stretch, managed to push it away.
Stoke manager Tony Pulis: "The longer the game went on I thought there was only one side that was going to win it.
"They were the better team in the first half hour but in the second half we were really disappointed we didn't put more chances away.
"I just thought the commitment in the second-half was first class."
Wigan manager Roberto Martinez: "It's always disappointing when you take the lead and can't get the three points but it's another point, that's the way we're thinking.
"In the second half Stoke came out with a lot of pressure and momentum.
"They put bodies forward, and to be honest the pitch didn't help us to get through that pressure."
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