Melbourne's Super Rugby AU season remains on a knife-edge after Rebels loss
The Rebels threw everything at the Brumbies in the second half but a knock-on stopped their attempt for a match-winning try three minutes after the fulltime siren.
Melbourne at least secured a bonus point, which may prove crucial with the last spot in the three-team play-offs to be decided in the final round next weekend.
That will go to either the Rebels or Western Force, with the Brumbies and unbeaten Queensland Reds already secure.
The final round will see the Force host the Reds on Friday night, and the Rebels play NSW in Sydney the following day and bonus points and points differential could end up deciding third spot.
That team will play the Brumbies in Canberra in the semi-final, with the Reds hosting the grand final a week later.
They started well, with a try to hooker James Hanson, before the wheels started to fall off.
The home side got that in check in the second half and started to get on top, with halfback Joe Powell bouncing off the defence to touch down two minutes after the break.
But their 19-7 halftime deficit proved tough to run down.
Rebels skipper Matt Toomua said he was “very proud” of the effort to stay in the fight.
“The scoreline probably didn’t reflect how we felt at halftime,” Toomua told Stan Sport.
“They probably had every right to be 20 up given the territory so we had a bit of energy going into halftime and that early try gave us some momentum.
“Ultimately our discipline hurt us.”
Sign up to our mailing list for a weekly digest from the wide world of rugby.Sign Up Now