The Cherries started with Pitman up front and set out to hit the hosts on the break. In the 29th minute Bartley broke forward and passed to Hollands to put the visitors a goal in front.
Partington was denied a second minutes later with Pearce sending a header just wide.
The second half saw the hosts apply more pressure, going close on several occasions. Pitman was sent clear by Hollands but was denied by a last ditch tackle.
With minutes remaining Abbott finally broke the Cherries stubborn defence to bring the hosts level. With seconds to go Pearce conceded a penalty to give Darlington all three points.