Rob Street scored a goal in each half and Luke Molyneux added a third as Grant McCann's men brushed aside a toothless Newport side who barely registered a sniff at goal.
The hosts came close in the early junctures with Street and Jay McGrath both warming the gloves of Newport stopper Nick Townsend. They were dominating chances and Owen Bailey saw two attempts go close before Luke Molyneux then produced a superb effort when he cut inside from the right but just saw his shot whistle past the left-hand post.
The breakthrough finally came just after the half-hour mark when Street prodded home from a few yards out after Newport failed to clear their lines from a corner.
And the hosts were celebrating a quickfire second barely 30 seconds after the restart. Molyneux crashed a shot against the woodwork. Street was quickest to react and after seeing Townsend deny his initial close-range attempt, he produced a cheeky backheel. Chances came and went for Rovers to build up their lead and Jordan Gibson nearly capped off a fine, free-flowing move midway through the half when he struck a post.
Molyneux then did land the killer third when he found the bottom-right corner after a lovely pick-out from Gibson and that's how it stayed.
Here's how we rated the Rovers players today:
5. James Maxwell 7
Restored in place of Anderson as McGrath moved back into the centre. Was positive in his play and didn't look to be too bothered by his broken toe. Photo: Howard Roe/AHPIX LTD
6. Owen Bailey 7
Busy in the engine room and was involved everywhere, marauding midfield as if his life depended on it. Came close with a few first half attempts. Photo: Howard Roe/AHPIX LTD
7. George Broadbent 8
Tenacious at the base of midfield, content to mop up any bits and pieces - as shown by the fact he racked up most tackles of any Rovers player. Photo: Howard Roe/AHPIX LTD
8. Harry Clifton 7
Plenty of running, hassling and harrying as Rovers won the midfield battle. Photo: Howard Roe/ahpix.com