They went at promotion hopefuls City almost from the off and the visitors were lucky not to concede after only seven minutes.
Pawel Abbott, signed from Swansea in the summer, looked to have increased his tally for the season to four when he found himself in space on the edge of the area and his first-time strike beat Lincoln keeper Alan Marriott before crashing against the crossbar.
Abbott and strike partner Tommy Wright have six goals between them so far and they both looked keen to increase their tallies as the Lincoln defence remained stretched.
Abbott prevented his side from taking the lead in the 30th minute when he stopped a certain goal by team-mate Julian Joachim almost on the goal line.
But Abbott struck four minutes later when he picked up possession following a poor clearance from keeper Marriott and he fired the ball left-footed into the bottom corner of the net.
Lincoln almost levelled three minutes from the break when Gary Croft fired inches over the crossbar.
The home side increased their lead seconds after the break when midfielder Ricky Ravenhill fired low from the edge of the area and the ball somehow found its way into the far corner of the net.
The visitors needed to change things around and a couple of substitutions livened things up. Winger Louis Dodds moved inside and he almost grabbed a lifeline in the 71st minute when he cut inside and sent a rising drive crashing against an upright. A minute later, Lee Frecklington went close from 20 yards.
Darlington ended the game the strongest and only a superb save from Marriott in the dying seconds of the game to deny Joachim kept the score line looking respectable.