Wallabies centre Pat McCabe was the first to score for the Brumbies in the 17th minute when he dived under the sticks from 10 metres out.
It sparked a flurry of activity from the home side, who then extended their lead to 23-6 after tries to Michael Hooper and Fardy - both within three minutes.
The Rebels, warned repeatedly for their infringements at the breakdown, then suffered another blow when referee Craig Joubert sin-binned skipper Gareth Delve 10 minutes before halftime.
Monster forward Fotu Auelua was unlucky not to be awarded a try moments later, but Brumbies skipper Ben Mowen made the most of the Rebels' mistakes by scoring from close range for a bonus-point try.
BRUMBIES 37 (Scott Fardy 2, Michael Hooper, Pat McCabe, Ben Mowen tries Christian Lealiifano 3 cons 2 pens) bt MELBOURNE REBELS 6 (Danny Cipriani, James O'Connor pens) at Canberra Stadium. Referee: Craig Joubert. Crowd: 14,011.
-AAP