The home side started strongly in Saturday's League One clash and were inches from opening the scoring in the 19th minute when a curling Alan Sheehan corner was glanced just wide of the far post by Jeff Hughes.
However, Swindon soon started to pile on the pressure and their best chance fell to James Collins after 22 minutes but his effort from Raffaele De Vita's cross was turned on to the post by goalkeeper Bartosz Bialkowski.
County took the lead against the run of play in the 28th minute when Judge collected the ball and planted a right-foot shot past a static Wes Foderingham in the Swindon goal.
The Magpies could have extended their lead after 54 minutes when new loan signing from Watford Chris Iwelumo rose highest to meet a Judge cross six yards out but Foderingham made a brilliant point-blank save.
However, one goal proved enough for Keith Curle's side to earn their first home win in seven attempts since September 22.
