Cheltenham maintained their unbeaten record but will be disappointed they did not go on to win the game after taking the lead just before half time.
Barnet pegged them back with a spectacular goal after the break and the visitors ground out a point despite a spirited late effort from the Robins.
The first half was low on goalmouth action as both sides, operating with five in midfield, attempted to play passing triangles with little end product.
Cheltenham goalkeeper Shane Higgs was called upon to save an early chance from Ismail Yakubu, although that was the young defender's last meaningful contribution before being forced out of the contest with an injury.
After a slow start the home team began to impose itself as the game wore on with midfielder John Melligan an influential presence playing just behind towering striker Kayode Odejayi.
It was Melligan who provided the ammunition for two good chances midway through the first half.
First defender Mike Townsend drew a fine save from goalkeeper Ross Flitney after Melligan had picked him out with a pinpoint cross.
Then a left-wing corner from the little Irishman was met by a power header from Michael Taylor that smacked the crossbar.
Higgs was forced to parry a shot from lone Barnet striker Giuliano Grazioli but it was Melligan again who provided the breakthrough just before half time.
Odejayi won the ball in midfield and fed Melligan wide on the right with the Barnet defence on his heels. Midfielder John Finnigan made a run into the box and met the right-wing cross with a header past Flitney to register his second goal of the season.
At that point the Robins were in control but Barnet came back at them with some controlled counter-attacking football in the second half.
They drew level on 56 minutes when Dwane Lee picked up possession 25 yards from goal and drilled a low shot past Higgs and into the bottom left-hand corner of his net.
After that the contest could have gone either way with Cheltenham substitute Damian Spencer dragging a shot wide and Higgs making a good save from Dean Sinclair.
Cheltenham almost grabbed all three points late on when another cross from Melligan was volleyed against the post by Spencer.