Barker, who saw a penalty saved when the two sides met in the League six weeks earlier, gained revenge one minute before half-time with the spot-kick which gave the Stags victory.
Leading scorer Barker had been the subject of frenzied transfer speculation in midweek following a rumoured £80,000 move to Hartlepool and news that the club was prepared to sell their talismanic striker also prompted new vociferous protests against chairman Keith Haslam from a section of fans throughout the tie.
But Barker ignored the rumours to hammer in his spot kick after Danny Ventre inexplicably handled Gareth Jelleyman's lofted cross.
Stanley, missing six injured first-team regulars, did include keeper Ian Dunbavin who saved two penalties in that thrilling 2-2 League draw.
And they almost took an early lead when Sean Doherty's curling free-kick sailed through a crowded penalty area on a blustery wind, but keeper Carl Muggleton came to the rescue.
Then Paul Mullin glanced a near-post header narrowly over from another Doherty cross, while Andy Mangan almost nodded in a third dangerous ball into the area from the wingman.
But the best Stanley chances of the first half fell to Ian Craney and Ventre, whose 20-yard piledrivers drew flying stops from Muggleton.
At the other end, Dunbavin repeated his heroics of September, saving spectacularly at the foot of the post to deny Johnny Mullins from a partially cleared Matt Hamshaw free-kick.
But he had no chance when Barker smashed the Stags in front in the 43rd minute.
A minute into the second half Craney almost hauled the visitors level but his low shot deflected narrowly wide in a crowded penalty area.
Michael Boulding's raking 25-yard effort was well held by Dunbavin as the home side looked to secure victory and then the keeper escaped punishment after a poor clearance went straight to the feet of Barker.
Dunbavin redeemed himself with a smart save to hold onto Jelleyman's deflected cross inside the six-yard area and then superbly hung on to a fierce close-range Boulding shot.
Those saves almost proved vital when Paul Mullin's low shot across the diving Muggleton grazed the outside of the post as Stanley stepped up the pressure in search of an equaliser.
In the last minute Craney again went close to an equaliser, but after getting himself into a good position, managed to fire his effort straight into the side-netting much to the delight of the nervy home fans.