Spencer Weir-Daley had given the visitors the lead against the run of play, but Lester equalised from close range in the second half.
The home side were left to rue their first-half profligacy as County went ahead on the stroke of half-time.
Weir-Daley punished hesitant defending when he took the ball past goalkeeper Barry Roche to score.
Lester hauled the hosts level after 59 minutes after good link-up play with Peter Leven.
Chesterfield then almost claimed all three points when Lloyd Kerry struck the crossbar with a 20-yard shot 18 minutes from time.