The Exiles secured maximum points after second-half goals from David Tutonda and Lee Minshull with Joe Day saving a Jake Hyde penalty in between.
The visitors had the best chances of the first half with Miles Storey lifting a simple chance over from eight yards after good work by Mark Byrne and Ryan Jackson.
Home keeper Michael Ingham also had to make a string of saves to deny Tutonda and Aaron O’Connor (twice) before the break.
But Tutonda opened the scoring on 50 minutes, shooting firmly past Ingham from 10 yards after Yan Klukowski had pulled the ball back from the byline.
Hyde went on to see a 62nd-minute penalty saved low to his left by Day after Klukowski had been penalised for a shirt pull on Keith Lowe.
Newport capitalised fully to secure maximum points when Minshull pounced from four yards with an unopposed header from Byrne’s inswinging left-wing free kick on 75 minutes.