Barnet came back strongly having been behind at half-time and thoroughly deserved to take away a point with their late equaliser.
The early exchanges had been pedestrian and were brought to life when Adam Gross upended dangerman Andy Parkinson in the Barnet penalty area for referee Rob Lewis to point immediately to the spot.
Lawrie Dudfield's initial strike was saved by Rob Burch and Barnet seemed to have escaped.
Then, after what seemed an age, the referee ordered the kick to be re-taken on the grounds that Burch had advanced off his line in dealing with the first effort.
This time Dudfield made no mistake by driving the penalty low to the goalkeeper's right.
Chances continued to be extremely limited for both sides despite the promptings of 41-year-old Andy Hessenthaler who controlled the midfield for Barnet.
County's next real chance was another penalty with Gross again fouling Parkinson and this time being cautioned as well.
Dudfield was again entrusted with the spot-kick only for his rising drive to cannon off the crossbar.
The longer the second half went, the more Barnet threatened and Kevin Pilkington had to make two saves from Jason Puncheon and Adam Birchall in turn when both strikers should have produced more testing finishes.
Then Barnet got their deserved leveller from a set piece with 16 minutes remaining.
A corner kick was swung in smartly from the left and from close range visiting skipper Nicky Bailey glanced the ball wide of Pilkington.
After that moment, Notts never seemed capable of finding a winning goal as Barnet finished by far the stronger.