Wildschut crossed for defender Reece Burke to put the visitors ahead from close range against the run of play.
Aaron Mooy equalised straight after half-time for the Terriers.
But Wildschut ran from inside his own half to round goalkeeper Danny Ward and slot home the winner.
The two teams came into the match at opposite ends of the table but both in poor form, with Huddersfield's early season dominance having fallen away in recent weeks.
However, the Terriers dominated the first half without finding the breakthrough, although Elias Kachunga did have an effort ruled out for offside.
Wigan had already looked dangerous on the break when they counter-attacked again and Wildschut sped down the right before delivering a centre for unmarked on-loan West Ham defender Burke to fire home.
Whatever Town boss David Wagner said at half-time clearly worked as five minutes into the second half, Mooy equalised after Nahki Wells' left-wing centre found him at the far post.
But Huddersfield had not learned their lesson when the Latics broke again and Wildschut ran unchallenged from the halfway line to round Ward and slot the ball home.
Wigan's first win in three games moves them up a place and although they are still in the relegation zone, it puts them level with Wolves on 18 points.
The Terriers are clinging on to the final play-off place but have now conceded 15 goals in their last six games, having only let in 10 in their opening 12 matches.
Huddersfield boss David Wagner told BBC Radio Leeds:
"We played some good stuff today, we brought our identity on the grass, created moments and played with speed and were energetic. It was a good game from my side, but unfortunately we didn't get two penalties in my opinion, after speaking with the guys from the TV one was 100%.
"Our biggest problem in our game was that we were not able to handle their counter-attacks better than we did.
"The first one we have to clear in the middle of the pitch, not when their winger was on the sideline, and the second one we switched off after we thought we had cleared the situation and the ball goes over our head.
"We have to give credit to our opponent. It was a gameplan Wigan had and it worked for them. They did exactly the same against Barnsley and we were not able to defend it better today."
Wigan boss Warren Joyce told BBC Radio Manchester:
"I'm obviously pleased to get the three points but it's just one game and you have to follow it up by bringing some consistency into the group, so we're seeing that regularly not only on a weekly basis but on a daily basis that we do the right things every day and then if you're doing that, there's a pretty good chance you are going to do it consistently on a Saturday or a Monday night.
"Yanic Wildschut is a very effective footballer. If he's got the ball at his feet or he's dribbling with it or he's running down the sides he's almost unstoppable at times. I just think he's a forward player that can play wide and I quite like him in that position so at the minute that's where you're looking to play him.
"Marcus Rashford played on the wing all the way through and it was a deliberate plan. I see similar similarities with Yanic's attributes, he's still a young player and he's got an unbelievable amount of pace and an unbelievable talent and if he wants to work hard and try and improve every day you don't know what the future could hold for him.
"One win doesn't really change anything about the situation we're in. We've got some really tough games coming up - tonight was a tough game where we've managed to get the three points."
Match ends, Huddersfield Town 1, Wigan Athletic 2.
Second Half ends, Huddersfield Town 1, Wigan Athletic 2.
Attempt missed. Luke Garbutt (Wigan Athletic) right footed shot from more than 35 yards misses to the right.
Luke Garbutt (Wigan Athletic) is shown the yellow card.
Corner,  Huddersfield Town. Conceded by Luke Garbutt.
Attempt missed. Philip Billing (Huddersfield Town) header from the centre of the box is too high. Assisted by Tommy Smith with a cross.
Corner,  Huddersfield Town. Conceded by Luke Garbutt.
Attempt blocked. Kasey Palmer (Huddersfield Town) right footed shot from the centre of the box is blocked. Assisted by Jon Gorenc Stankovic.
Substitution, Wigan Athletic. Craig Davies replaces Yanic Wildschut.
Corner,  Huddersfield Town. Conceded by Dan Burn.
Corner,  Huddersfield Town. Conceded by David Perkins.
Attempt saved. Max Power (Wigan Athletic) right footed shot from outside the box is saved in the centre of the goal. Assisted by Stephen Warnock.
Substitution, Wigan Athletic. Nick Powell replaces Nathan Byrne.
Tommy Smith (Huddersfield Town) wins a free kick in the defensive half.
Foul by Yanic Wildschut (Wigan Athletic).
Attempt missed. Michael Jacobs (Wigan Athletic) right footed shot from the left side of the box is high and wide to the right. Assisted by Yanic Wildschut.
Elias Kachunga (Huddersfield Town) wins a free kick on the right wing.
Foul by Michael Jacobs (Wigan Athletic).
Substitution, Wigan Athletic. Dan Burn replaces Reece Burke.
Tommy Smith (Huddersfield Town) is shown the yellow card for a bad foul.
Foul by Tommy Smith (Huddersfield Town).
David Perkins (Wigan Athletic) wins a free kick in the attacking half.
Attempt blocked. Christopher Schindler (Huddersfield Town) header from the centre of the box is blocked. Assisted by Chris Löwe with a cross.
Corner,  Huddersfield Town. Conceded by Reece Burke.
Attempt missed. Tommy Smith (Huddersfield Town) right footed shot from outside the box misses to the left.
Attempt blocked. Philip Billing (Huddersfield Town) left footed shot from outside the box is blocked. Assisted by Nahki Wells.
Substitution, Huddersfield Town. Philip Billing replaces Jonathan Hogg.
Attempt missed. Rajiv van La Parra (Huddersfield Town) right footed shot from the left side of the box misses to the right following a corner.
Corner,  Huddersfield Town. Conceded by Michael Jacobs.
Foul by Aaron Mooy (Huddersfield Town).
Shaun MacDonald (Wigan Athletic) wins a free kick in the defensive half.
Foul by Chris Löwe (Huddersfield Town).
Yanic Wildschut (Wigan Athletic) wins a free kick in the attacking half.
Attempt missed. Nahki Wells (Huddersfield Town) right footed shot from the right side of the box is too high. Assisted by Aaron Mooy.
Goal!  Huddersfield Town 1, Wigan Athletic 2. Yanic Wildschut (Wigan Athletic) right footed shot from the centre of the box to the centre of the goal. Assisted by Max Power with a through ball following a fast break.
Elias Kachunga (Huddersfield Town) wins a free kick on the right wing.
Foul by Michael Jacobs (Wigan Athletic).
Attempt missed. Aaron Mooy (Huddersfield Town) right footed shot from more than 35 yards misses to the right from a direct free kick.
Rajiv van La Parra (Huddersfield Town) wins a free kick in the attacking half.
Foul by Michael Jacobs (Wigan Athletic).
Yanic Wildschut scored one goal and made another as Wigan earned their first win under new manager Warren Joyce and stretched Huddersfield's winless run to four games.