The Blues went ahead on 37 minutes when Steve Nicholson headed the ball beyond his own goalkeeper under pressure.
But the lead didn’t last long with Kane Reece finishing well past Mike Hale to level things up four minutes before the break.
Jacob Davis headed Darren Peacock’s side back in front 10 minutes after the restart from a corner.
Again the visitors couldn’t hang onto their lead however and Albion were on level terms for a second time on 67 minutes.
A move down the right ended with Rob Bordman squaring for Ross Hardaker to convert from close range.
The result leaves the Dolly Blues 10th in the Evo-Stik First Division North ahead of their game against Burscough at Giant Axe on Tuesday night.