Cian Hughton, the son of Newcastle boss Chris, headed the Imps in front after 25 minutes at Sincil Bank from a perfect Delroy Facey cross to claim his first goal in the Football League.
Lincoln doubled their lead just four minutes later when Facey looped another header over the stranded Mark Crossley.
Lester, however, was unlucky to see a header of his own come back off the crossbar a minute before half-time.
Chesterfield dominated possession after half-time and got the goal their pressure deserved when substitute Scott Bowden smashed home a right-footed shot seven minutes from time.
The visitors were then given a chance to rescue a point when Lincoln defender Adam Watts brought down Drew Talbot, but Lester smashed his 87th-minute spot-kick over the bar.