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The Red Imps looked to be heading for defeat after conceding a first-half goal.
But they hung on despite strong Derby pressure and the game turned on a controversial 78th minute penalty decision.
Referee Keith Hill harshly ruled that Spanish midfielder Inigo Idiakez handled a cross from Michael Blackwood despite Derby's protests. When things died down Gary Taylor-Fletcher sent County keeper Lee Camp the wrong way from the penalty kick to net his fifth goal of the season.
Derby were still stunned two minutes later when Lincoln sub Francis Green fired in a low cross. The ball went straight through the centre of the Derby defence and Simon Yeo was left unmarked to score at the far post.
Derby definitely tried to change things by introducing Ian Taylor and Junior but instead fell completely apart.
Yeo was only denied his second goal of the game by a tremendous tackle from Tom Huddlestone.
But in stoppage time the Imps put the result beyond doubt when Taylor-Fletcher skipped past four defenders before sending over a low cross which was converted by Jamie McCombe.
Derby began well with Lincoln pushed back early on and Paul Peschisolido was denied by an 11th minute save from Lincoln keeper Alan Marriott before County took the lead.
Lincoln's Blackwood was yellow-carded for fouling Peschisolido on the edge of the box and Idiakez blasted a 28th minute free-kick in off the bar.
Derby at times threatened to over-run Lincoln but found Marriott in top form.
The keeper got down well to push out a 56th minute shot from Adam Bolder.
Marriott then produced excellent saves to keep out Lee Holmes and Idiakez.
But Lincoln began to show what they could do in the 66th minute when Camp could only push out a shot from Peter Gain.