A first win in five league matches kept AFC in touch with the play-off places in the North West Counties League first division.
READ MORE: Stockport Town 0 AFC Blackpool 0
New Mills hammered AFC 4-1 in Derbyshire this season but this was a much closer affair at the Mechanics Ground.
Although the visitors looked the more likely scorers for much of the first half, midfielder Danny Pickering went closest for the home side but his header from an inswinging free-kick was well saved by New Mills keeper Oliver Martin.
Despite plenty of pressure from New Mills, it was AFC who took the lead in the 40th minute when captain Martin Baird picked up the pieces from a free-kick to score from six yard.
AFC were much improved in the second half, substitute Alex Taylor twice going close as he hit bar and post, while winger Billy McKenna saw an effort saved by Martin.
AFC remain in eighth spot, four points behind sixth-placed Cammell Laird 1907 but with four games in hand, the first of which is scheduled for Carlisle City on Tuesday (7.45pm)
Blackpool: Kirkland, Donaghy, Betteridge, Cassidy, Baird, Pickering, Bishop, Hargreaves, Duffield, Williams, McKenna