The U's squandered two good chances in a very scrappy first half. James Constable finished with a weak shot in front of goal after a mix-up between two County defenders, and then headed Danny Rose's corner over the bar from four yards.
Newport had plenty of the ball but found it hard to create scoring opportunities other than from set pieces.
They threatened at long throws, and from one free-kick, Lee Minshull's backheader drifted just wide. Ismail Yakubu also went close with a header at a corner.
County's ex-Oxford centre back Harry Worley was lucky to escape with a yellow card after a dreadfully late challenge on Ryan Williams.
Justin Edinburgh's team have now gone five matches without conceding a goal. Indeed, they almost snatched all three points as Christian Jolley fired against the top of the bar on the counter-attack six minutes from time.