The Potters took the lead in the 23rd minute when Ryan Shawcross capitalised on a Latics defensive blunder to hook the ball in, and Peter Crouch made it 2-0 in the 48th, following up Charlie Adam's parried shot.
At that point Stoke looked on course for what would have been their first victory in five league matches, but two minutes later James McArthur pulled a goal back for the visitors by completing a neat move and Franco Di Santo then levelled with a 61st-minute volley.
The result sees Wigan move from 19th place up to 17th in the table, level on points with 18th-placed Aston Villa, who lost 2-1 at home to Newcastle on Tuesday night, while Stoke stay 10th.
Potters boss Tony Pulis had mentioned in the build-up to the game how Wigan - who the Staffordshire outfit had beaten only once since gaining promotion to the Premier League in 2008 - were "something of a bogey team" for his side and in his formation for the contest, he opted to match the Latics' defensive structure, playing with wing-backs either side of three centre-halves.
It looked in the early stages as if he might have to adjust the personnel he had selected at the back when a nasty collision of heads between Robert Huth and Di Santo led to a stoppage of several minutes.
Huth appeared to have come off worse and seemed set to be substituted, but after being bandaged, like Di Santo he continued playing.
On a pitch made slick by a spell of heavy rain, it was Stoke who then settled quickest, with Jon Walters skewing an effort wide and Wigan league debutant Roman Golobart having to make a clearance to prevent a flick-on from reported QPR target Crouch reaching Adam.
Adam then drilled the ball just the wrong side of the post after collecting a pass from Matthew Etherington.
A tame Di Santo effort was all Wigan could muster in response and moments later the hosts' pressure yielded a goal.
Adam delivered a free-kick into the box and Jean Beausejour attempted to clear it but could only nod the ball against team-mate James McCarthy, sending it into the path of Stoke skipper Shawcross who finished from close-range to register his first goal of the season.
The lively Adam then saw a dipping effort evade the top corner, before Wigan began to show a greater threat towards the end of the first half, with one cross from Beausejour cannoning behind off McArthur and another being spilled by Asmir Begovic, which no-one could take advantage of before a clearance was made.
The Potters were back in the ascendancy at the start of the second half, doubling their lead within three minutes of the restart.
Latics January signing Roger Espinoza gave the ball away and Stoke's resulting break saw Adam hit a low shot which Ali Al Habsi parried, allowing Crouch - who had not scored since September - to slot in.
Wigan's reply was virtually immediate, with Espinoza making a more positive contribution by sliding in a through-ball which McArthur clipped home delightfully.
And after Adam had struck a free-kick wide, Espinoza's redemption continued as he fashioned a cross which McArthur headed back for Di Santo to volley in.
It then required a great save from Begovic to deny McArthur as Wigan looked to complete their comeback.
Stoke substitute Cameron Jerome subsequently wasted a chance to win it for his side and Di Santo met a cross in front of goal late on, but was just unable to guide the ball in as the fixture finished 2-2 for the fifth time in 10 meetings.