Under new boss Christian Fuchs, the Exiles held their own during an entertaining but goalless first half, but their resistance was finally broken eight minutes into the second half.
Michael Mellon's header was saved by Jordan Wright, who could only parry it as far as Josh Hawkes who netted.
Ex-Newport loanee Joe Quigley doubled the lead from close range after receiving the pass from Kane Drummond who was helped by good work from substitute Mike Fondop in the build up.
Hawkes sealed the victory with a minute remaining when he fired across the face of goal and into the corner of the net.
Latics, who had only scored 13 goals in their previous 16 league games, are 15th in the table while County remain rooted at the bottom.
Latics boss Micky Mellon saluted double hit-man Hawkes after the game.
He said: "Josh is such a talented lad, I'm really pleased that we've got him here.
"He was a well deserved man of the match."
