The former Arsenal striker smashed home from close-range after the Albion defence failed to clear Jason Puncheon's corner.
It was rough justice on Nigel Clough's men, who had seen Keith Gilroy smash an effort against the Barnet crossbar, while Shaun Harrad slumped to the ground after seeing an effort ruled out for offside.
And despite a late onslaught from the visitors, the Bees held on to keep their dreams of FA Cup glory alive into the new year.
Despite failing to win in their past six league games, Barnet showed no signs of fragility in the opening few minutes with Birchall enjoying his return to the starting line-up in place of the suspended Liam Hatch.
The striker went close on two occasions in the opening few minutes, forcing Burton goalkeeper Kevin Poole into a sharp save before seeing his first-time effort blocked by team-mate Ashley Carew.
Barnet's ability to move the ball quickly and into space was clearly causing the Blue Square Premier side some problems.
And Paul Fairclough's men should have made their early dominance pay, but Giuliano Grazioli failed to convert from close-range after Michael Leary's effort had deflected into his path.
With time ticking down towards half-time, the visitors would have been more than happy to enter the warmth of the dressing room level, but they were almost caught cold by Birchall.
A long ball into the Burton penalty area caused panic among the visitors backline, but the Bees striker could only fire his effort against the outside of the post from a tight angle.
The second-half started much like the first with Barnet on the attack and looking menacing in front of goal.
With both teams looking to find that elusive goal, large gaps began to appear in the midfield allowing both sets of forward players more freedom.
Poole once again had to be in top form to tip Birchall's rasping drive over the crossbar, while Harrad saw his effort ruled out for offside at the other end.
With the game seemingly drifting towards extra-time and with neither side looking remotely capable of finding the net, it was with great relief to the home faithful that their side finally made the breakthrough.
Puncheon's right-wing corner caused confusion in the Albion backline, allowing Birchall time to swivel and fire low past the outstretched arm of Poole.