Kane Hemmings had struck just before the interval – his long-awaited first goal for Mansfield in his ninth appearance - and it was looking like the Stags were set to end a run of two straight defeats.
However, Barnet struck late as Coulthirst, on loan at Mansfield last year and only declared fit before the game, expertly dispatched a rebound.
The Bees looked the more lively of the two sides in the early stages.
Veteran Jamal Campbell-Ryce tested Stags ‘keeper Conrad Logan early on when his 25-yard strike was well saved.
However, the visitors soon gained a foothold and created some great chances of their own before the half-hour mark.
The Stags were thwarted twice in rapid succession. Danny Rose’s acrobatic effort was frantically hacked off the line, with Alex MacDonald’s rebound was superbly saved by Bees ‘keeper Craig Ross.
As the Stags continued to press, Kane Hemmings found plenty of space in the Barnet box, only to fire disappointingly wide.
Shortly before the break David Mirfin went close when he met MacDonald’s corner-kick, but he headed over the top.
Hemmings broke the deadlock seconds before the whistle, diverting home from close range after MacDonald slipped as he was in the process of shooting.
Hemmings almost made it two shortly after the restart. However, his shot was blocked by an over-stretched Campbell-Ryce.
Midway through the second period the Bees began to pile on the pressure.
Mauro Vilhete powered in a super which was expertly saved by Logan.
Ricardo Santos also saw a strike blocked as the Stags were hanging on to their slender lead.
The pendulum began to swing back in the Stags’ favour in the latter stages, with Hemmings again being thwarted by a great stop from Ross.
However, Coulthirst was to have the final say as the Stags at least ended up taking home a point following back-to-back defeats.
Conrad Logan also came up with a superb stoppage time save to keep out Clough’s header and preserve that point.