Oxford's 1-1 draw with Fleetwood Town on Saturday offered Paul Cook's men the opportunity to leapfrog them at the summit.
Nevertheless, the Spireites failed to capitalise on the slip-up and ultimately ended the contest with ten men following the dismissal of Liam Cooper on 74 minutes.
The Welsh outfit, who now sit eighth in the table, one point adrift of a playoff position, took the lead through Danny Crow after just six minutes.
Jimmy Ryan hit back for the visitors midway through the second half to preserve his team's hopes of replacing The U's at the top of England's fourth tier.
Despite the numerical disadvantage Chesterfield valiantly went in search of an equaliser, but Newport countered and killed the game off in the dying stages through Andy Sandell.