Padraig Amond came back to haunt former club Grimsby with a goal on 63 minutes to secure a 1-0 victory for Newport.
The visitors cleared the ball off the line seven times during the first 40 minutes in a half dominated by Mike Flynn's side.
Keeper James McKeown was responsible for saving Grimsby on three occasions, with left-back Ben Davies, Mitch Rose and Paul Dixon making last-gasp clearances that also saved the Mariners.
Newport have had a good start to the season - winning six of their opening nine Sky Bet League Two games under manager Flynn - and were completely dominant in this encounter.
The home side exerted all the early pressure with McKeown forced into a double save from shots by Mark O'Brien and Amond.
Finally a concerted period of pressure from the hosts finally broke the resolve of Russell Greenslade's side when Amond hit the ball into the net from close range against his former employers.
Grimsby pushed for an equaliser late on but Newport's defence remained resilient.