Robert Bordman scored both goals for the visitors, opening the scoring after 22 minutes and then converting a penalty five minutes before the break.
Victory lifted Albion up to 19th with Town falling to 11th.
At the top of the division, Farsley Celtic’s perfect start was ended as they were held to a goalless draw at new boys Tadcaster Albion, who sit seventh. Farsley remain top but now only one point clear of Brighouse Town, who obliged 2-1 at Colwyn Bay.
Adam Field gave Brighouse a 12th-minute lead, which was doubled by Jamie Frost six minutes after the break. Luke Denson’s 65th-minute penalty then set up a grandstand finish. Prescot Cables are a point further back in third after romping in 5-0 at Burscough.
Honours were even at Goole AFC who bagged their first point of the season thanks to a 1-1 draw with Scarborough Athletic. Lee Morris put Goole ahead after 22 minutes, but Carl Stewart equalised for the visitors 19 minutes from time. Scarborough now sit 13th.
In the Premier, Frickley Athletic’s miserable start to the season continued – six games, six losses – as they were hammered 4-0 at Whitby Town for whom Dale Hopson converted two penalties.