The visitors rarely threatened and have now won only one of their last 14 matches.
Cheltenham’s depleted defence was under pressure from the offset and it took a goal line clearance from Josh Low to deny Rob Page in the 13th minute.
But the visitors cracked two minutes before half-time when Lester was left unmarked at a corner to score with a near post header.
Lester headed another good chance wide as Chesterfield continued to dictate but they were given a warning in the 78th minute when Theo Lewis forced Mark Crossley into his first save with a 25-yard shot.
Chesterfield sub Scott Boden was denied a second goal in stoppage time when Scott Brown saved with his legs.