Finley Potter and Ryan Graydon earned Fleetwood their first away victory since August to leave Newport still rooted to the bottom of Sky Bet League Two.
Exiles winger Michael Spellman, who was later sent off for two yellow cards, went within inches of netting the opener after 20 minutes when he cut in from the right and thundered a shot against the crossbar from 25 yards.
At the other end, County goalkeeper Jordan Wright pulled off an impressive point-blank save to keep out Potter’s header.
Just as it looked as though honours would be even at the break, Christian Fuchs’ men were twice caught cold at the back.
In the 44th minute, they allowed Potter to sneak in at the far post to head in an Ethan Ennis cross from close range.
And, in the fourth minute of first-half stoppage time, Mark Helm put Graydon through on goal after a quick break and he danced around the defence before coolly beating Wright.
