Peter Vincenti fired Dale ahead just five minutes in with a stunning long-range drive. He collected a loose ball 35 yards from goal, took a step forward and unleashed a rising drive which flew past Lenny Pidgeley.
The home side doubled their advantage in the 38th minute. Ian Henderson and Joe Rafferty combined on the right to set up Jamie Allen whose shot from eight yards hitting the crossbar. Graham Cummins seized on the rebound, turned and fired a low drive past Pidgeley.
Newport wasted a great opportunity to get back into the game on the hour mark when Jack O'Connell was penalised for a challenge on Conor Washington and referee Steven Rushton awarded a penalty. But Adam Chapman's spot kick was blocked by Josh Lillis' legs.
The home side made the result safe with third goal in the 71st minute, substitute Bastien Hery had been on the pitch a matter of seconds when he collected Vincenti's pass, rounded Pidgeley and slotted home.
Henderson hit the post and Pidgeley pulled off a good save to keep out Matt Lund's shot as Rochdale dominated the closing stages.