The Bees have to settle for a point on the road, following a hard-fought clash with the Minstermen.
A first half goal from John Akinde earned Barnet a share of the points, following an entertaining match at Bootham Crescent.
Lewis Alessandra put the Minstermen ahead in the 20th minute after a strong start from the home side.
But Akinde converted James Pearson’s pinpoint cross in the 37th minute to take home a share of the spoils.
It was York who began the game strongly, and had the first chance of the match after just two minutes.
Jake Hyde connected with a knockdown from a York corner, but his off balance shot floated over the crossbar.
A minute later Dave Winfield’s bullet header flew wide of the left post from another York set piece.
The Bees responded in the 12th minute – Akinde picked up a neat pass from Luke Gambin, before firing a shot over from the edge of the box.
Luke Summerfield met a Femi Ilesanmi corner on 15 minutes, but his effort flew wide of the left post.
York’s early pressure paid off when they took the lead mid-way through the first half.
A shot from former-Bee Hyde cannoned off the post, before the rebound was slotted home by City debutant Alessandra.
The Rochdale loanee had another low effort saved by Jamie Stephens soon after, before Barnet started to find their way back into the match.
York needed a goal-line clearance from Luke Hendrie to keep them ahead in the 22nd minute, when Akinde rolled a shot past the advancing Scott Flinders.
Then Gambin latched onto Pearson’s ball over the top on the half hour mark, only to put his shot narrowly high and wide of the goal.
The Bees finally levelled things up when Akinde met Pearson’s low cross from the right; firing past Flinders in the 37th minute.
Barnet had a further chance just before the break - Gambin burst down the left and hit a powerful shot just wide of the left post.
The Minstermen took the game to Barnet during the early stages of the second half.
Stephens tipped Hyde’s looping header over the bar in the 49th minute, before turning Alessandra’s shot behind for a corner immediately after.
The Bees’ keeper then acrobatically palmed Danny Galbraith’s 53rd minute free kick over the crossbar.
Once again Barnet responded, and Sam Togwell could have put them ahead when his right-sided shot was deflected agonisingly wide of the left post.
Eliott Johnson whipped a cross into Akinde, but his 67th minute header ended up just wide of the goal.
However it was some late heroics from Stephens that ended up keeping Martin Allen’s side in the game – the goalkeeper got down well to save from Alessandra and then Bradley Fewster in the final minutes of the match.
In the end both sides had to settle for a point, following a frenetic and pulsating encounter.
Barnet face Oxford United at The Hive next Saturday.
BARNET: Stephens, Pearson, Nelson, Sesay, Johnson, Yiadom ©, Togwell, Champion (Shomotun 70’), Randall (Vilhete 60’), Gambin (Batt 86’), Akinde.
Subs Not Used: McKenzie-Lyle, Muggleton, Gash, Roberts.