County, who started the day as joint leaders in League Two, dominated the early exchanges, but their hard work was undone on 25 minutes when Northampton broke the deadlock with their first meaningful attack of the game.
On-loan forward Blyth, who signed from Leicester City yesterday, headed home from 12 yards following a fantastic run and cross by Ian Morris.
The lead was doubled just two minutes later when more magic from Morris set up Roy O'Donovan, who converted a simple tap-in from close range.
Northampton put the result beyond doubt on 86 minutes courtesy of Deegan's first goal for the club.
Deegan beat goalkeeper Jamie Stephenson with a driven effort that was cleverly assisted by O'Donovan.
Newport youngster Conor Washington netted a consolation goal to complete the scoring in the dying seconds.