A Chris Lines free kick from 25 yards drew Rovers level on 39 minutes and four minutes later the midfielder struck again with a superb shot from the edge of the box.
A foul by Danny Coles allowed Alex Revell to net Wycombe's second penalty on 46 minutes and Beavon came up with the winner, powerfully nodding past Mikkel Andersen.
Rovers had a loud penalty claim themselves in the closing stages when an Andy Williams shot was blocked in the box, but referee Rob Shoebridge was not interested.
Jo Kuffour shot narrowly wide for the home side as injury time approached, but Rovers could not break through again.
Source: Team Talk