Gritton had suffered an early-season goal drought, going 15 games without getting on the scoresheet, but his double means he has now scored five in seven games.
His first on 23 minutes was a classic strike, jinking inside and out of lumbering centre-back Robert Page before planting a 15-yard shot inside the far corner.
Macc extended their lead two minutes later when Lee Bell pounced on a mistake by Kevin Austin before clipping a 20-yard shot into the net.
However, captain Sean Hessey let Chesterfield back into the game with a mistimed header to his keeper which allowed Jamie Ward to power home a low drive from 15 yards.
Gritton added his second on 53 minutes as he collected a pinpoint pass from Bell, controlling neatly with his first touch and burying a clinical finish with his second touch.
But Chesterfield responded on 68 minutes when Ward shrugged off marker Izak Reid before powering home a 12-yard shot. Macclesfield sealed the game on 83 minutes when sub Gareth Evans beat keeper Trevor Carson to the ball.
The match was marred by a double sending-off in injury-time as Macc sub Francis Green had a pitchside boxing match with marker Alan Goodall.
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