The visitors tried to force an early goal as Sjoerd Overgoor played the ball through for Deniz Turuc just a few minutes after kickoff, but the striker's finish lacked power, leaving Filip Kurto with an easy stop.
The Dordrecht keeper continued to come under early pressure as Jeffrey Rijsdijk created some space on the edge of the box, but Kurto was able to prevent the goal again.
After a quiet start to the second half, Xandro Schenk almost handed Dordrecht the lead when he put too much on a header back to Mickey van der Hart, but the keeper just managed to prevent the own goal.
The hosts looked the more likely midway through the second half, but Van der Hart denied Lieder before Job van der Linden turned a free kick over.
Joris van Overeem had a chance to secure all three points for Dordrecht late on after bursting through from the edge of the box, but he scuffed his finish wide.
However, the hosts kept pressing, and their efforts paid off when Sean Klaiber headed the ball in off the underside of the crossbar in stoppage time.
Despite picking up all three points, Dordrect remain rooted to the foot of the table, while the Eagles sit 15th.