The 41-year-old midfielder, who captained the side in the absence of Ian Hendon, steered in a Tresor Kandol cross from six yards after Barnet had fallen behind to a Peter Gain goal for a Posh side bidding to end a run of four successive home defeats.
Posh just about took the honours in an undistinguished opening half that often lacked creativity.
Lee Harrison advanced to go down and save at Danny Crow's feet early on, although the former London Road goalkeeper then failed to reach a Jamie Day corner and was relieved to see a Richard Butcher shot crash into a pack of players.
Barnet were comfortable on the ball without producing any really penetrating moves. Ben Turner cut out the danger when Liam Hatch threatened and Mark Tyler saved comfortably after full-back Nick Bailey broke forward on the left.
Kandol wasted a glorious 32nd-minute opening when failing to hit the target with a left-footed shot, and the miss was compounded when Gain broke the deadlock two minutes later.
The one-time Spurs midfielder lifted the ball into the top right hand corner after a Day shot rebounded off Harrison's legs.
Kandol almost redeemed himself by sending a shot dipping on to the roof of the net as the interval approached and the hard-working Hatch saw a snap effort held by Tyler.
The second half was barely a minute old when Hessenthaler hauled Barnet level, before Dean Sinclair missed a great chance to put the North Londoners in front, failing to get his shot past Tyler after finding himself in a one-on-one situation.
Trevor Benjamin went close with a 15-yard drive that Harrison spectacularly tipped over and former Barnet man Mark Arber, a late Posh substitute, almost snatched a winner with an added time header that smacked against the crossbar before Adam Gross booted the ball clear.