Chesterfield's pace and power in attack opened the visitors up in the 13th minute when Dean Morgan's cross was headed in at the back post by Lester.
Morgan almost set up a second before Stockport stunned the home side with a long ball that put George Donnelly in and his second attempt found the net off Dwayne Mattis.
Craig Davies was foiled by an excellent save from Matt Glennon in the 49th minute but Lester restored Chesterfield's lead in the 62nd minute.
The 35-year-old striker turned and glided away from three challenges before lifting the ball over the keeper and he bagged his third five minutes later after Glennon had parried a Davies header.
Davies sealed an impressive second-half display with a 20-yard shot for his 15th of the season in the 90th minute.