The Rams, rejuvenated since ex-England boss Steve McClaren returned, stunned their opponents as Craig Bryson, Simon Dawkins and Chris Martin all found the net before the half-hour mark.
Derby have lost just once since McClaren became manager in September and tore apart a team who could still qualify for the Europa League's last 32 at will.
Latics manager Owen Coyle will by heartened by the second-half response, started by Nick Powell's sixth goal of the season, yet the mountain from which the fightback began was too steep.
Up until this clash, Coyle had handled the extra demands of European football with Wigan taking 10 points from a possible 12 in Championship games after Europa League clashes.
A raft of changes each time had worked but the decision to pick Ivan Ramis, out since January with a knee injury, and Manchester United loanee Will Keane, making his first ever professional start, appeared bold.
Neither had a chance to ease themselves in. Just two minutes had gone when centre-back Ramis was cleaned out as he got caught up in Powell's wild slide challenge on Dawkins.
With Ramis stood on the touchline receiving treatment, Bryson stepped up and bent the free-kick into the top corner.
Things went from bad to worse when, in a similar area of the field to Powell's foul, Ben Watson gifted the Rams a second goal 12 minutes after the opener.
The midfielder inexcusably slipped a pass straight into Dawkins' path and the winger took a couple of touches before sliding beyond Lee Nicholls.
The home supporters, who prior to last week had not seen a defeat at the DW Stadium in this campaign, were shellshocked yet the visitors were in no mood to sympathise.
A quick counter-attack ended with James McClean tripping Martin in the box, the striker then sending Nicholls the wrong way from the spot to hand Derby a three-goal lead with 16 first-half minutes still to play.
The one saving grace for Wigan was that they still had 11 men, perhaps only the case because referee David Coote displayed leniency when giving Watson a yellow card for a knee-high swipe at Johnny Russell.
The away fans mischievously claimed Coyle was getting sacked in the morning, a chant which, worryingly, was applauded by certain sections of the home faithful.
They were not able to console themselves with a goal before the break either, Stephen Crainey's free-kick cannoning off the crossbar.
However, Grant Holt and Roger Espinoza were brought on for the second half and a response soon materalised.
Emmerson Boyce had already gone close himself when his cross was headed home by Powell four minutes after the restart.
And Coyle's half-time words clearly had the desired effect, James McArthur almost adding another when he nodded narrowly wide before Holt's cross was inadvertently flicked on to the bar by Jake Buxton.
Now under the cosh, Derby were perhaps fortunate that John Eustace's elbow-led jump on Powell warranted just a yellow card.
There was no lasting damage to Powell, though, as he showed with a volley which produced a fine one-handed stop from Lee Grant.
That save sucked the life out of Wigan's fightback, although Grant was twice called upon in stoppage time, allowing McClaren's men to move up to fifth.