City struggled to create any chances and in the end were well beaten by the Quakers.
Darlington started well and almost scored after only four minutes when a mistake let in Rob Purdie, who beat home keeper Rob Burch with his shot, only to see the ball come back off the post.
Three minutes later, Purdie set up what proved to be the decisive goal when he fired in a cross from the right.
Danny Carlton was allowed to steal in unmarked and sent a looping header over Burch into the back of the net.
Lincoln briefly threatened midway through the first half with Dany N'Guessan firing in two dangerous crosses, but Lincoln were unable to take advantage.
Darlington always looked the more likely team to find the net and should have scored in the 35th minute. A powerful shot from Tim Ryan brought an excekllent save from Burch. The ball fell into the path of Carlton but wth an empty net in front of him, the striker fired wide.
Lincoln appeared to be denied a penalty five minutes before the break when Aaron Brown burst into the box and was tripped by Ryan Valentine, but referee Carl Boyeson rejected appeals for a spot-kick.
The game became very scrappy in the second half with Lincoln pumping the ball forward aimlessly in a desperate attempt to get something out of the game.
Substitute Adrian Patulea rose at the far post to meet a cross from N'Guessan, but headed wide.
Carlton then wasted another superb chance for Darlington ten minutes from time. The striker found himself unmarked inside the box, but shot straight at Burch, who made a point-blank save.
Lincoln almost sneaked an equaliser in the second minute of stoppage time. Paul Green's 50-yard free-kick dropped inside the six-yard box but Ben Wright scrambled his shot against the outside of the post.