After only four minutes striker Gregg Blundell found himself inside the area and, with only keeper Andy Warrington to beat, looked certain to score.
However, he missed the chance and soon afterwards Blundell was again denied by the Rotherham keeper.
The visitors went close in the 19th minute and should have done better when Derek Holmes connected with a cross from Ian Ross, but the striker somehow put his free header high over the crossbar from ten yards out.
The game was open and, in a quick break forward in the 22nd minute, Julian Joachim saw his low cross intercepted by Ian Sharps and then, three minutes later, Pablo Mills went close for Rotherham with a 25-yard drive.
In the second half O'Grady headed narrowly over in the 56th minute with a good 12-yard effort and, seven minutes later, Quakers midfielder Richie Foran was lucky to escape with only a yellow card after a two-footed lunge on Marc Joseph.
The home side grabbed an equaliser in the 68th minute through Michael Cummins. Blundell crossed from the right flank and Cummins turned sharply inside the area to fire home beyond Warrington's despairing dive.
Rotherham tried to respond and, in the 71st minute, Darlington keeper David Stockdale finger-tipped a volley from Holmes around the post.
As time began to run out, it was Darlington that ended the game strongest and, in the 83rd minute, Rotherham captain Graham Coughlan did well to block a shot from Cummins.
Two minutes later Coughlan almost deflected a low cross from Foran into his own net before Darlington substitute Pawel Abbott fired against the crossbar three minutes from time.