Stevenage were taken all the way but the point now means that a win over Forest Green will see Boro make the play-offs.
The home side made all the early running with Jon Nurse twice coming close in the opening 20 minutes, while George Boyd saw a shot pushed across the face of goal by keeper Chris Porter.
York took the lead against the run of play and their goal on 37 minutes also lead to Stevenage's first sending off.
The home side protested after Clayton Donaldson hit the ball in for the opener from what appeared to be an offside position.
Their fury was increased when Darryn Stamp was dismissed for a second yellow card after protesting with a linesman.
Stevenage looked for the leveller and came close before the break when Dino Maamria saw a shot parried wide and from the resulting corner Jason Goodliffe fired Stevenage level with a volley into the top corner.
Stevenage continued to push forward with both Nurse and Maamria testing keeper Porter, while at the other end Donaldson was booked for dissent after he appeared to have been pulled down in the area.
With the referee adding seven minutes of injury time, Stevenage were reduced to nine men when Goodliffe was given a straight red after protesting at York for time wasting.