Both sides went close before Knoyle settled the contest just shy of the hour mark with his first goal of the season and second in 77 games.
Right-back Knoyle, who played in a back three in Tom Anderson's absence due to illness, leathered the ball home from the edge of the box following Ben Close's cutback.
The win halted Rovers' two-game losing streak in League Two and moved them up to tenth and within two points of the play-offs.
1. Match action
Harrison Biggins goes close in the first half. Photo: Howard Roe/AHPIX LTD
2. Jonathan Mitchell - 7
In the right place at the right time to stop Newport from opening the scoring through Will Evans prior to Knoyle's winner. Collected several dangerous deliveries too. Photo: Pete Norton
3. Charlie Seaman - 6
Offered a good outlet down the right-hand side on his first start since October. Photo: Howard Roe/AHPIX LTD
4. James Maxwell - 7
A solid defensive display and much improved going forward. Photo: Howard Roe/ahpix.com