The New South Wales Waratahs, who play the Chiefs away and sixth-placed Hurricanes at home, are in fifth spot, just one point ahead of the Brumbies, who host the Highlanders next week and then finish with the Crusaders in Christchurch.
The Reds, who had a mathematical chance heading into Saturday night's clash of seizing top spot on the ladder, suffered a massive double blow, losing both their second-rowers to injury inside the opening 25 minutes.
Adam Byrnes limped off with an apparent ankle injury before Rob Simmons sustained a suspected fractured cheekbone. Not surprisingly, the Queensland lineout was in disarray, with the Brumbies stealing a series of Reds throws.
But it was the powerful Brumbies scrum which caused the Reds most pain.
Both the Brumbies' first-half tries - to lock Mark Chisholm in the 13th minute and Alexander 10 minutes later, came after skipper Stephen Hoiles opted for attacking scrums on the Queensland line instead of gift penalty goals.
After trailing 14-10, Queensland clawed their way into the contest with two penalty goals from five-eighth Quade Cooper in the 26th and 33rd minute.
Two more Cooper penalties after the break narrowed the deficit to two points, but the Brumbies secured a deserved victory with further tries to halfback Josh Valentine in the 56th minute and Alexander seven minutes from fulltime.
- AAP