It meant David Wagner’s side remain sixth in the Championship and badly need a pick-me-up performance at Blackburn Rovers on Saturday to get their season back on track.
It was the first time Schindler had failed to start since joining in a club-record £1.8m move from 1860 Munich during the close-season.
Wigan arrived second-bottom with only three victories this season and still seeking a first win under manager Warren Joyce -the Latics had never won a league match in Huddersfield in 12 attempts.
A season-ending knee injury for on-loan Liverpool keeper Adam Bogdan meant 41-year-old former Finnish international Jussi Jaaskeliainen was, as expected, between the posts for the visitors.
As it happened, Schindler came off the bench just seven minutes in as Hudson was forced off by a hamstring injury.
By that stage, Wigan defender Stephen Warnock had been booked for a foul on Scannell.
Elias Kachunga came closer in the eighth minute, heading onto the roof of the net from van La Parra’s cross, then Stankovic headed just wide from an Aaron Mooy free-kick.
Jonathan Hogg was yellow carded for an 18th-minute foul on Nathan Byrne.
Van La Parra had a shot deflected off target before Kachunga nodded home only for Tommy Smith, who delivered the cross, to be ruled offside.
Jaaskelainen denied Lowe when the left-back shot hard and low, then pushed away a Kasey Palmer header.
Palmer then put a shot from outside the area narrowly wide before a cross from the Town right only just evaded the stretching Kachunga with the goal gaping.
Wigan were quick on the break, however, and Danny Ward had to get down low to deny Wildschut on 38 minutes.
Dutchman Wildschut was the architect of Wigan’s opener five minutes before half-time, breaking down the right and skipping past Stankovic and Mooy to tee up Burke for the finish.
Town made a second substitution after 44 minutes, with Wells replacing Scannell, who had looked in discomfort since the early foul by Warnock.
Wildschut continued to pose problems, and Ward pushed his shot away in first-half stoppage time.
Wells had a header saved before his strong run and pass set up Mooy to level things with a close-range finish five minutes into the second half.
Mooy stung Jaaskelainen’s hands with a long ranger soon after as Town tried to pick up the pace, but there was a big setback for the home team on the hour.
Wildschut raced through on the counter and kept his composure to round keeper Ward and put the visitors back in front.
To rub salt in home wounds, referee Tony Harrington then turned down a Wells penalty appeal after a challenge by Warnock.
Town made their third change after 67 minutes, when Philip Billing replaced Hogg, and the final substitute soon unleashed a stinging shot which was deflected off course.
A 72nd-minute caution for a foul by Tommy Smith means the right-back will be suspended at Blackburn Rovers on Saturday after reaching five for the season.
Schindler made an important block from Max Power, allowing Ward to collect his shot. Town forced a couple of late corners, but to no avail.