Vale's first opportunity came in the 32nd minute through Louis Dodds but the forward's weak effort from 20 yards was easily collected by goalkeeper Jake Cole.
John O'Flynn was inches away from scoring on the stroke of half-time but his low effort was brilliantly saved by Chris Martin to ensure the sides went in level at the break.
The hosts continued to press after the interval and spurned glorious chances through O'Flynn and former Chelsea striker Paul Furlong. Both came after good work down the right by the industrious Yannick Bolasie.
Barnet pushed for a winner in the closing stages but Micky Adams' men held on for a fortuitous point despite seeing skipper Tommy Fraser dismissed late on for a professional foul.