A brace from Chris Zebroski and goals from Harry Worley and Christian Jolley handed Justin Edinburgh's newly-promoted side a dream start to life in League Two.
Danny Webber scored a consolation for Stanley but that failed to stop the party mood in south east Wales following Newport's first game back in the top four divisions since they faced Rochdale on May 7, 1988.
The home side went ahead at a sun-kissed Rodney Parade in the 23th minute when Worley, on his debut, volleyed home after the Accrington defence failed to deal with David Pipe's long throw.
Newport doubled their advantage three minutes before the break courtesy of fellow debutant Zebroski.
Adam Chapman released Jolley down the right flank and his driven cross was converted from close-range by the striker.
Yet the best goal was still to come. In the 55th minute Jolley curled a superb left-foot effort beyond goalkeeper Ian Dunbavin and into the far corner.
Zebroski added a fourth for Newport with an excellent volley in the 66th minute before Webber fired home from close-range two minutes later to round off the scoring.