Jack Lester's 20th league goal of the season gave the home side a first-half advantage but Adrian Patulea's 11th of the campaign earned the visitors a point.
Chesterfield had the chances to win the game but Lincoln defended impressively and Rob Burch made an excellent save to deny Lester a second.
Both teams went into the match fancying their chances of making the play-offs although Lincoln realistically needed to win to close the gap.
Skipper Scott Kerr twice broke through only for Tommy Lee to save at his feet and Burch was also called into action when he clawed away a Martin Gritton header in the 29th minute.
But Lester showed why he is rated as one of the top strikers in the lower leagues in the 35th minute when his right-foot shot from 14 yards had the accuracy to nestle in the bottom right-hand corner after Peter Till had crossed low from the right flank.
Lincoln had had their moments and they came out fired up after the break and were level in the 52nd minute with former Chesterfield defender Janos Kovacs involved.
The big defender got on the end of a corner from Michael O'Connor and, when the ball dropped to Patulea, he blasted the ball in from close range.
Anthony Elding had an excellent chance to put Lincoln in front four minutes later but his hesitation at the back post allowed Lee to block his shot and the action switched to the other end with Chesterfield rattling the bar from a Gregor Robertson free-kick in the 58th minute.
Lincoln were now coming under increasing pressure and, in the 74th minute, Till put Lester clear but Burch got his angles right to plunge low to his left to deny the striker a second.
Lincoln had moments on the break with Dany N'Guessan failing to make the most of two promising openings and Chesterfield also went close near the end.
Jamie Lowry had a shot charged down and Till also saw a fierce drive blocked but Lincoln held on for a result that gives them an outside chance of making the play-offs.