In the opening seconds of the game home midfielder Jason Kennedy volleyed over the crossbar from the edge of the area. The former Middlesbrough midfielder fired over from a similar position two minutes later, as the home side went on the offensive from the start.
Bradford looked to have weathered the storm, but as the rain fell, the hosts wasted another good chance when striker Billy Clarke found captain Steve Foster free in the box. The defender fired high into the stand from ten yards out in the 14th minute.
City began to get their passing game together and in the 23rd minute Joe Colbeck darted into the area before firing across the face of goal with the ball going aimlessly wide when the slightest of touches from a team-mate would have put the visitors in front.
Darlo came back again in the 36th minute and City had keeper Rhys Evans to thank, as he reacted well to push away a stooping header from defender Alan White.
Bradford began the second half on the attack and former Darlington striker Barry Conlon slid in at the far post but failed to connect with a right-wing cross from Colbeck in the 47th minute.
Colbeck then went close with a volley from 18 yards that shaved the top of the cross bar after 53 minutes. Ten minutes later City boss Stuart McCall made a change when bringing on Omar Daley for Kyle Nix.
The winger's pace down the left began to cause problems for the home defence, but the breakthrough just wouldn't come for either side.
Darlington midfielder Rob Purdie missed a sitter in the 75th minute when, with only keeper Evans to beat, he screwed the ball wide from eight yards out.
The hosts did take the lead though in the 84th minute when defender Neil Austin's free-kick flew past Evans and into the roof of the net.
The lead lasted for less than a minute as substitute Daley raced in from the left and saw his low shot squirm under keeper Simon Brown and into the back of the net.
As the game moved into the 90th minute Purdie crossed from the right and Franz Burgmeier rose inside the area to power a header beyond Evans and seal all three points for the home side.