Despite leading for most of the match, Cheltenham can console themselves in extending their impressive run of form that has brought only one defeat in 17 games.
With their current away form so positive, it was perhaps little surprise that Cheltenham started the brighter of the two sides and took an early lead on eight minutes.
David Bird advanced down the left flank before crossing towards the penalty spot and John Melligan met the pull back with a wonderfully controlled right-foot volley that fizzed into the roof of the net.
Conceding an early goal seemed to spark the home side into life and Barnet almost forced their way back into the game on 12 minutes.
Lee Roach pulled the ball back across goal where the unfortunate Liam Hatch could do no better than graze the woodwork after sliding in at full stretch to connect with the cross.
The impressive Ben Strevens was then unlucky twice in the space of two minutes.
First when his run and low shot from the left drifted agonisingly wide of Scott Brown's left-hand upright and then again with another left-footed strike that was gathered comfortably by the keeper.
Following a subdued performance by both sides at the start of the second half, it was Strevens again who nearly brought Bees level two minutes after the restart.
The striker rose highest to connect with Ian Hendon's free-kick but his deft header missed the target by millimetres with Scott Brown rooted to the spot.
With just over 10 minutes left on the clock and with Barnet seemingly heading for defeat, Strevens turned provider.
Substitute Giuliano Grazioli profited from his strike partner's inch-perfect cross and headed powerfully past Brown at his near post.