Barnet showed the greater ambition in the opening stages and were brimming with confidence having won their last two games.
In the eighth minute midfielder Richard Graham released Birchall through the middle, Craig Morgan held up the striker superbly forcing him to play Adam Gross in down the flank. His shot hit the target but lacked any venom to trouble goalkeeper Paul Rachubka.
Peterborough's response was immediate and could have been telling but for a timely intervention by Ismail Yakubu. Richard Butcher found Danny Crow through the middle but the Barnet trainee recovered well and nearly sent Crow into the stand.
Barnet deservedly broke the deadlock on 13 minutes, Barry Cogan passed into the feet of Birchall on the edge of the area. Morgan appeared to be in control of the situation. However, with his back to goal the striker turned and shot in one motion with a fierce drive that went in off the crossbar from 16 yards.
Barnet continued to probe but the visitors missed a great chance to equalise. On 33 minutes Ross Flitney failed to deal with a Jude Stirling thrown-in, he punched straight to Butcher but was able to thwart the midfielder's goalbound effort from 11 yards out.
In the second half play moved from end to end in a competitive game that was only to interrupted by some dubious officiating.
On 56 minutes Barnet moved from their own penalty area to Peterborough's in three passes. Joe Devera released Cogan down the wing, the midfielder combined brilliantly with Birchall in the box, but the Mansfield loanee dragged his shot from eight yards wide of the right-hand post.
Dean Sinclair then missed a gilt-edged chance when he lobbed over the bar from 12 yards.
Peterborough showed little evidence of their promotion-challenging qualities and should have fallen further behind when substitute Liam Hatch failed to cap a glorious move, missing from two yards in the game's dying seconds.