The result pushed the Quakers out of the top seven and they now face an uphill task if they are to get in the play-offs themselves.
Darlington came looking for a draw and started with just one man up front. Their unadventurous approach produced just a single shot on target throughout the 90 minutes and they only showed any urgency after learning that their play-off rivals Northampton were ahead at Chester.
Lincoln almost snatched the lead after just three minutes when Gareth McAuley got on the end of a Simon Yeo cross but his effort was blocked by keeper Sam Russell.
Three minutes later Kevin Sandwith floated over a long free-kick and McAuley stole in unmarked at the far post only to be denied again by Russell.
Sandwith was inches away from breaking the deadlock in the 12th minute when his inswinging corner left Russell stranded but Jonjo Dickman cleared off the line.
Darlington swept upfield and worked the ball to Clyde Wijnhard but the striker's low shot was saved by the diving Alan Marriott.
Lincoln had a great chance in the 28th minute when Ben Futcher headed on a long throw but striker Derek Asamoah headed over from inside the six-yard box.
Peter Gain then sent Gary Taylor-Fletcher clear but he produced a weak shot which Russell saved easily.
Lincoln created the better chances and in the 54th minute leading scorer Yeo sent over a cross which Richard Butcher was inches away from converting.
With 23 minutes left Darlington decided to push men forward with substitute Akpo Sodje coming on to partner Wijnhard.
The Quakers went close to winning a 77th minute penalty when Dickman appeared to be fouled inside the box by Futcher but referee Mark Cowburn turned down appeals for a penalty.
Darlington pressed forward in the final minutes without really causing any problems for Marriott.
And Lincoln almost sneaked a winner in the 88th minute when Peter Gain forced his way into the box only for Russell to beat away his shot.