Green volleyed the Stags ahead from edge of the area, while Liam Noble sent Notts' best first-half chance wide.
Adam Chapman doubled the advantage with a curled free-kick into the top corner before Green pounced on a Mike Edwards error to make it 3-0 soon after.
Reggie Lambe added a third goal in 10 minutes and Mitchell Rose made it 5-0.
Mansfield's second league win over Notts this season sees the Stags move up to 12th in the table and and to within three points of the top six, with the rest of the day's League Two fixtures kicking off at 15:00 BST.
Matt Green scored twice as Mansfield recorded their biggest Nottinghamshire derby win against Notts County to keep their League Two play-off hopes alive.