The Magpies went close after nine minutes when Connell Rawlinson headed a cross from Enzio Boldewijn back across goal and the ball hit the post, before the Dutchman then saw his free kick crash against the crossbar.
Chesterfield were awarded a penalty in the 39th minute for a foul on David Buchanan by Alex Lacey but Notts keeper Ross Fitzsimons saved Scott Boden's spot-kick down to his left.
The home side took the lead in the 51st minute when Boldewijn charged forward and slammed a 20-yard effort into the top corner of the Spireites net.
Notts doubled their advantage lead just before the hour when Kyle Wootton headed in and the striker tapped home a third goal with 15 minutes left after Boldewijn's effort was saved.
Here is what Pride of Nottingham's ARLukomski made of the game, in his latest vlog:
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