The Stags went ahead in first-half stoppage time with a goal from Michael Boulding, a one-time Huddersfield trialist, and secured their deserved win immediately after the interval.
Huddersfield boss Peter Jackson was fuming that Barker's goal was allowed to stand with Simon Brown clearly in an offside position.
Brown was jogging back when the ball was punted forward, and seemed to block keeper Matt Glennon's view, before Barker robbed Nathan Clarke, drew Glennon and slotted home.
This victory was some measure of revenge for Mansfield, still unbeaten this season, for the last time these two sides met - in the League Two play-off final at Cardiff in 2004, Huddersfield were successful, being promoted on penalties.
There might have been only one Mansfield player still in the side from that day two years ago - defender Alex Baptiste - but this win clearly meant everything to them.
Huddersfield sent out a virtually full-strength side, only without captain Jon Worthington with a groin injury, but were never comfortable.
Danny Schofield went closest to scoring for the home side in the first half but keeper Jason White tipped away his drive from outside the box.
Gary Taylor-Fletcher gave the ball away and allowed Brown to centre for the unmarked Stephen Dawson who completely missed his kick a minute before the break.
Two minutes into stoppage time Huddersfield centre-back Nathan Clarke failed to clear and his header backwards fell to Boulding who flicked the ball over Glennon. Clarke flung himself on the line but to no avail.
Barker then sealed it just after the break and Mansfield, with strike duo Brown and Barker on fire, ran Huddersfield ragged for a 15-minute spell.
The home side needed to thank Glennon for keeping the score down. First he beat out Brown's dipping effort and then Matty Hamshaw's corner was met by the unmarked Barker but Glennon saved on the line.
Huddersfield brought on Andy Booth to add strength up front but he fared little better than Pawel Abbott and Luke Beckett.
Mansfield boss Peter Shirtliff replaced Brown to protect the lead but Huddersfield had nothing left, and trooped off the field to a chorus of boos.