Darlington took a deserved lead on 42 minutes when Lincoln keeper Alan Marriott made a complete mess of his punch from a Martin Smith corner.
Marriott somehow managed to deflect the ball behind him and against the post for Darlington defender Darren Holloway to score with the easiest of finishes.
The goal was no more than Darlington deserved as they dominated the first half.
Midfielder Clark Keltie shot wide after just 11 minutes and Darlington striker Alun Armstrong should have scored four minutes later but he failed to make the most of a mistake by Lincoln defender Adie Moses and missed the target from 8 yards out.
Smith and Darlington forward Simon Johnson both missed good chances before Holloway put the visitors ahead. Lincoln went looking for the equaliser after half time and young winger Leon Mettam shot inches over the bar.
But Darlington put the game beyond doubt when they doubled their lead on 53 minutes when the Lincoln defence failed to clear a free kick from the edge of the box.
Michael Cummins was first to react and beat Marriott with a left foot shot from 12 yards out.
Darlington grabbed the third on 72 minutes when Johnson made the most of an awful mix-up in the Lincoln defence to coolly slide the ball home from close range.
Lincoln again came under pressure when Darlington defender Craig James tried his luck with a free kick from 30 yards out. The powerful effort looked to be heading for the top left hand corner until Marriott produced a brilliant fingertip save to tip the ball over his bar.
Lincoln grabbed a consolation goal on 82 minutes when left back Paul Mayo pounced on the ball on the edge of the Darlington box and unleashed an unstoppable drive which gave Darlington keeper Sam Russell no chance.