The only way to win a Rook versus Knight ending (playing the side with the Rook) is if the Knight is driven too far away in order to intervene to what will essentially be a Rook versus lone King endgame OR the Knight gets trapped on the edge of the board and then captured.
In both cases, the opponent's King and Knight must be separated, while your own King will need to be strategically placed near the piece getting mated/captured... An opponent knowledgeable of the endgame will be able to prevent this 100% of the time, given enough time on the clock. An exception occurs when the Knight is in one of the 4 corners (or 1 square diagonally from each of those), where its mobility is greatly reduced. Then, not even a nearby King will be able to help it from being captured.
I've been working on an endgame study which covers some of this, see the analysis in the chapter below (unfortunately can not link to positions in variations). Hopefully it can be of use to others as well.