Bradford City's heavy win over Colchester United helped ensure Grimsby took Colchester's place in the play-offs
George McEachran's second-half free kick sent Grimsby Town into the League Two play-off spots.
The hosts dominated possession and had vastly more chances than The Exiles.
But it took until McEachran's clinical 64th-minute strike to break broke Newport's resistance.
Having lost their two previous encounters, Grimsby now find themselves sixth while Newport stay 16th.
Newport boss Nelson Jardim: "It's always frustrating when you lose, never a good feeling. But I think we've worked on a couple of things, and we've tidied up a couple of things when we play away and I think we showed that we were hard to beat. I think for spells we defended well.
"It's just frustrating, especially the way you've we've conceded the goal, again after a set play and those set plays are costing us a lot of points away.
"Today was another one, but it's just a deflection and there's not much you can do about that."
