The Reds looked headed for an easy victory against the misfiring Brumbies when they dominated possession in the first 30 minutes in Canberra and shot to a 15-0 lead.
However, the Brumbies notched their third win from six outings this year by running in the last six tries of the match to secure a bonus point as the Reds imploded.
The Reds, who beat the Brumbies in week three, dominated the game until Folau Fainga'a scored the home side's opening try after a driving maul against the run of play in the 27th minute.
That was the turning point. Isireli Naisarani added their second try in the 34th, and the Brumbies remarkably could have been in front at the break, with a second Fainga'a try denied by the video referee when he was ruled to have touched the side line with his foot as he dived over in the corner.
That meant the Reds led 18-12 at half-time but they did not fire a shot thereafter.
Chance Peni, Rory Arnold, Naisarani, Sam Carter and David Pocock added further tries for the Brumbies in the second half as Australia's only finalist in 2017 took total control.
Brumbies co-captain Christian Lealiifano said they reaped the rewards of sticking to their game plan after the tardy start.
"We made it tough early but proud of the boys to really stick it out," he said. "It was real sloppy from us at the start."
In Hamilton, New Zealand, a late penalty try saw the Chiefs sneak home over the Blues 21-19 after trailing for much of the match.
In Tokyo, the NSW Waratahs ran in seven tries and picked up a bonus point by thrashing the winless Sunwolves 50-29.
The Chiefs lost playmaker Damian McKenzie after half an hour and the Blues rallied to hit the front 19-14 by half-time, a lead they held for 35 minutes until a costly yellow card saw their scrum falter seven minutes from the final whistle.
The result lifted the Chiefs to five wins from six games while the Blues sank to one win from six.
The Blues defended heroically for most of the second half to protect a five-point lead until lock Jack Goodhue was yellow-carded and an underpowered Blues scrum conceded the match-winning seven-point penalty try for the Chiefs.
The Blues have not won away against the Chiefs since 2011 and captain James Parsons lamented a lost chance.
"Ill-discipline has cost us the game, the yellow card... we were down a man and they took it to us and got the penalty try," Parsons said.
The Waratahs, meanwhile improved their record to four wins and a draw from six games and are second in the Australian conference behind the Melbourne Rebels.
Scrum-half Jake Gordon bagged two tries as the Waratahs ran in seven tries to four.