The Imps had all the possession but could not find a way through a packed Carlisle defence.
And as Carlisle grew in confidence they always looked capable of sneaking a winner on the break.
City went close after just three minutes when Colin Cryan picked out Gary Birch with a deep cross but the striker saw his header tipped over by Anthony Williams.
Three minutes later Nat Brown fed Derek Asamoah who cut in and fired in a low shot which Williams saved at his near post.
A superb save by Williams prevented Lincoln from taking the lead in the 15th minute. Midfielder Scott Kerr crossed for Brown whose downward header looked a certain goal until Williams somehow scooped it off the line.
The lively Asamoah was causing Carlisle plenty of problems and in the 36th minute his cross found Marvin Robinson whose overhead kick was kept out by the impressive Williams.
Carlisle finally ventured forward in the 38th minute and from their first corner almost grabbed the lead. Lincoln failed to clear their lines and the ball came out to Zigor Aranalde whose powerful shot smashed against the post.
Then Kevin Gray chipped a pass into the Lincoln box but Karl Hawley just failed to collect.
A shot from Asamoah was fumbled by Williams but no Lincoln player was near enough to take advantage, then in first-half stoppage time, City appeared to be denied a clear-cut penalty when Robinson was wrestled to the ground.
Referee Dean appeared to be unsighted and United got a let off.
A great 49th minute save by Williams kept out Robinson but Carlisle increasing pulled men back to frustrate Lincoln and even wasted a couple of chances in breakaways.
Peter Murphy got in a 67th minute cross and Brendan McGill forced his way past his marker only to head wide.
Soon after Chris Billy won a challenge outside the box and set up McGill but the midfielder hit his shot straight at Lincoln keeper Alan Marriott.