Jamie Cooke and Drew Cheshire crossed along with a penalty try and 16 points from the boot of Lee Millar.
Yorkshire Carnegie lost 29-19 at London Scottish, their six-game winning run coming to an end. Mike Myerscough, Josh Bainbridge and Andy Forsyth scored tries, with Alex Davies adding two conversions.
However, they can still qualify for the quarter-finals as one of the best runners-up, depending on their result at home to Jersey on Saturday.