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:
1. Ted Sharman-Lowe 6
Can't imagine he will have had too many quieter days than this. Barely anything to trouble him. Photo: Tony Johnson
2. Jamie Sterry 8
Another solid showing, with some excellent, raking pick-outs to Street. Second half saw him up his performance as he contributed to plenty of attacks. Photo: Howard Roe/ahpix.com
3. Joseph Olowu 7
Hardly troubled in fairness. Did what he had to do with the minimal of fuss or bluster. Photo: Howard Roe/ahpix.com
4. Jay McGrath 7
Had a rare chance when his fierce shot was tipped behind for a corner. Got done by Ajiboye early on but more often than not he came out on top in their duels thereafter. Photo: Howard Roe/ahpix.com