A frenetic opening saw both chances for both sides. The visitors came within inches of opening the scoring in just the second minute as Adam Rooney on the stretch just failed to connect to Elliott Bennett's inviting cross.
Bennett then saw his header from Nicky Adams' cross bring out a comfortable save from Lee Harrison in the home goal.
At the other end, Anthony Thomas brought the home support to its feet with a sublime piece of skill followed by a stunning 30-yard shot, unfortunately for him it was straight at Jim Provett in the Shakers' goal.
Still though Bury pressed. Rooney should have done better when Bennett did well to pick him out, as he produced a tame finish.
The half ended with a glorious chance for the Bees, but Albert Adomah, unmarked at the far post, headed Nicky Nicolau's cross wide.
Thomas should have put the home side ahead minutes after the restart though having tuned well in the box, horribly skewed his effort wide.
Birchall then headed over from Jason Puncheon's, cross, but he made amends soon after when bundling his way through two challenges, he then managed to flick the ball past Provett for his tenth league goal of the season.
He claimed his 11th of the season with 20 minutes remaining as substitute Cliff Akurang set him up for a simple finish to end the game as a contest.
The roles were reversed nine minutes later as Birchall was denied a hat-trick by a superb save by Provett and Akurang was on hand to tap home the loose ball.