Jamie Forrester scored two first-half goals in as many minutes as the Imps came from behind and were then forced to hold on after Danny N'Guessan was dismissed 21 minutes from time.
Chester had only themselves to blame after missing a host of chances, starting with Kevin Ellison's poor spot-kick in the fifth minute, which was saved by Alan Marriott after the keeper had felled John Murphy.
Paul Linwood headed over from a corner and then Mark Hughes twice wasted great opportunities as Chester passed up a succession of chances which could so easily have had the game sewn up inside the first 15 minutes.
Marriot, who up to that point had had an eventful opening in the game, left the field on 16 minutes to be replaced by Aiden Duffy, seemingly after injuring himself in the course of giving away the penalty.
Chester's pressure was finally rewarded on 20 minutes as Paul Rutherford's low cross from the right flank was swept home by Paul McManus.
The lead lasted seconds as the game was turned on its head with two goals in quick succession. First, persistence by Forrester saw him shrug off Linwood and bundle the ball home from close range on 21 minutes.
And then in the 23rd minute a long ball upfield was nodded into the path of Forrester by Ben Wright and he stuck the ball past the onrushing John Danby for his second of the game.
On the stroke of half-time Forrester had a chance to complete his hat-trick when he again linked up with Wright, but the Chester keeper produced a brilliant stop to deny the striker.
The second period saw Chester pushing for a leveller and they were given hope when the visitors were reduced to ten men as N'Guessan received his marching orders following a second booking for a late challenge on Laurence Wilson.
Twelve minutes from time Chester sub Glenn Rule struck the bar with a volley and Linwood missed his kick when he looked odds-on to score.
Ellison was then denied by a great save by Duffy late on as the Imps held firm.