The first effort on goal from either side fell to Darlington midfielder Jason Kennedy in the seventh minute but his 25-yard drive went inches over Frank Fielding's crossbar.
Two minutes later Pawel Abbott turned inside the area and drove narrowly wide after collecting a pass from Neil Austin. Abbott drove across the face of Fielding's goal in the 13th minute as Darlington kept up the pressure.
Ciaran Toner cleared a dangerous inswinging free-kick from Franz Burgmeier in the 18th minute after Fielding spilled the ball on his six-yard line.
Rochdale pressed forward and captain Gary Jones brought a tip over the crossbar from Dean Gerken in the Darlington goal with a fierce volley in the 19th minute.
Against the run of play Rochdale took the lead in the 28th minute through Adam La Fondre who picked up Scott Wiseman's pass inside the Darlington area and his shot gave Gerken no chance as it flew into the far corner of the net.
Darlington were forced to make a substitution in the second half when Hatch was injured following a clash with Fielding. Hatch left the field on a stretcher and Danny Carlton replaced him in the 53rd minute.
In the 60th minute Abbott put Darlington level with a close-range shot following Rochdale's failure to clear a Burgmeier corner to the near post area.
Rochdale regained the lead two minutes later when Adam Rundle collected a throughball from the impressive La Fondre and fired a low drive from ten yards past the stranded Gerken in the Darlington goal.
The Quakers were reduced to ten men in the 63rd minute when midfielder Ricky Ravenhill was shown a red card after a two-footed challenge on Wiseman and the home side were unable to force themselves back into the game.