The Blues were heading for a win moving into stoppage-time until Blunden turned the ball in after an almighty goalmouth scramble.
Harpenden had plenty of territory, but Dunstable managed the game well, and didn’t look under any particular threat.
The home side saw more joy down the left, with Adam Sawyer seeing a fierce shot blocked well, while Charlie Weatherhead and sub Harvey Scott both fired over for the visitors.
Five minutes from half-time Dunstable were ahead when Davide Pobbe firmly headed Dan Blackman’s in-swinging cross beneath keeper Alex Desmond.
Harpenden ramped up the pressure after the break, with Scott squandering Harpenden’s first clear chance of the game when he failed to make clean contact with a cross into the box, and Dan Gould saved easily.
But minutes later it was 1-1 when Gould received a backpass under pressure and dealt with it well, but the ball came straight back and Nathan McGreevy slotted into the bottom corner.
The Harpenden attacks came in waves, with Gould doing well to tip Blunden’s free-kick over the bar.
Having been the better side in the second half, Harpenden trailed again with five minutes left.
Once again, Blackman’s corner created the opportunity, this time for Joe Hankins arriving in space to guide his header into the net.
But the visitors would not be denied a deserved point.
Dunstable headed to Leverstock Green on Tuesday in the Dudley Latham Premier Cup, and travel to Biggleswade United on Saturday in the league, before the club’s quiz night at Creasey Park that evening.