Blyth, a recent signing on loan from Leicester, netted after 25 minutes and his strike partner Roy O'Donovan quickly extended the lead two minutes later.
Gary Deegan ensured all three points for Aidy Boothroyd's side with six minutes remaining but there was still time for substitute Conor Washington to reply for the visitors.
Looking to build on their opening-day success, newcomers Newport created some decent early openings.
Matt Duke tipped over Christian Jolley's deflected cross and from Adam Chapman's subsequent corner the Cobblers goalkeeper got the faintest of touches to help Chris Zebroski's header on to the crossbar.
More was to come from the Welsh club as Max Porter fired just wide, Zebroski failed to convert David Pipe's loss cross and Ismail Yakubu headed over.
In between, Blyth was just off target as the hosts finally created an opening.
But, after surviving County's initial threat, Northampton took the lead in the 25th minute when on-loan striker Blyth rose superbly to head home an inswinging cross from Ian Morris.
The Cobblers doubled their advantage shortly afterwards with Morris once again the provider, this time playing in O'Donovan who neatly curled the ball around keeper Jamie Stephens and into the far corner of the net.
Newport had a couple of chances either side of the break to reduce their arrears. Duke kept out another Zebroski header on the stroke of half-time and Pipe shot wide just after the restart.
Boothroyd's team again started slowly in the second half and rarely threatened but Deegan added a third goal in the 84th minute, latching on to substitute Ivan Toney's pass to beat Stephens with a low effort from the edge of the box.
Sub Washington grabbed an 89th-minute consolation goal when he cut into the box before beating Duke from a tight angle.