Peterhead kept their excellent recent run going with a crucial win that puts them above Partick Thistle in third place on goal difference.
The Blue Toon dominated for long spells but failed to take their chances, mainly thanks to some inspired goalkeeping from Albion's Myles Hogarth.
Peterhead went close after four minutes, Martin Wood crossing for Bobby Linn who saw his point-blank header tipped over for a corner by Hogarth.
The home side went in front in the 11th minute. Woods' shot was deflected into the path of Kevin Nicol, who scored at the second attempt after his first shot was blocked by Hogarth.
The keeper was in action again a minute later, acrobatically diving low to his right to turn away a Wood shot.
Albion had plenty of the ball but rarely looked like finding the net, Connolly lobbing wide before home keeper Paul Mathers made a double save from Connolly then Steven Bell.
Peterhead should have doubled their lead after 53 minutes, Linn cutting the ball back for Wood, but Hogarth clawed his shot clear.
The game burst into life again after 58 minutes, Stirling defender Mark McNally brought down Wood inside the area, who was red-carded for his protests. Linn took the resulting penalty, but man-of-the-match Hogarth saved, then blocked Linn's follow-up effort.
Twenty minutes from the end Peterhead tied up the points with a superb solo effort from Graeme Sharp. He ran more than half the length of the pitch before cutting inside and finishing with a low shot into the net by the far post.