In a first half of few clear opportunities, Nathan Cartman's low shot was kept out well by Gregory Hall, who also claimed an early Neal Bishop header, while skipper Harry Coates had a header scrambled clear.
Coates also made the challenge of the first half with an expertly-timed challenge to deny Jo Maswali when he was clear through on goal on the edge of the penalty area.
Boro opened the scoring on 54 minutes from the penalty spot after a foul on Kian Spence, Nathan Cartman scoring at the second attempt after the first seemed to be ruled out for encroachment.
The visitors seemed to be drifting out of the game with Boro looking to be in control, but 10 minutes from time sub Connor Heath headed in at the far post after the Boro defence switched off, bringing the scores level.
The Dabbers almost stole an undeserved win in the final minute as Dave Webb's free-kick fizzed wide of Ryan Whitley's goal, but both sides had to settle for a point.