Noble scored the opener and, after substitute Tahvon Campbell equalised for Rovers, Matt Tootle netted the winner with 10 minutes remaining to leave County third in League Two, two points above Wycombe.
Noble pounced in the 34th minute, touching home inside the box in a dour first half.
Rovers had to wait until the 23rd minute to register their first shot on goal – Reuben Reid drawing a save from Adam Collin.
Manager Mark Cooper shuffled his Forest Green pack after the break and his side levelled things up after 72 minutes with a stunning goal from Campbell. Reid teed the West Brom loanee up and he put Carl Dickinson on the floor before hitting a rising strike over Collin.
Rovers were on top and Campbell had the bit between his teeth, fizzing an effort against the crossbar from the edge of the box just three minutes later.
Rovers pressed the self-destruct button after 80 minutes. Tootle took aim in the box with the ball going through the hands of Chelsea loanee Brad Collins to seal the win.
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.