Mickey Boulding’s 22nd goal of the season on 14 minutes proved to be the difference between the sides in the first half.
And when Matty Hamshaw lobbed Lee Harrison on 55 minutes, it seemed the Bees were buried.
Stags striker Jefferson Louis had two great chances to seal the win with close range headers, but the first went wide and the second saw Harrison turn the ball onto his post.
Home keeper Carl Muggleton was not kept busy until the Bees threw on Birchall, Jason Puncheon and Anthony Thomas on 68 minutes. Within two minutes Thomas had buried a low 20-yard shot.
And after 77 minutes Puncheon’s free-kick came back off a post and Birchall reacted to sweep home the loose ball.