Skipper Sam Cane said of the fightback: "It's like we cranked up a notch and we were like, 'right, now we're here to play', which is ridiculous. I wish we could try and work on getting that from the first whistle, so that we had a focus.
"In a funny way it'll be good to come in Monday, nut it out together, take what we can so that it doesn't sort of just get brushed under the carpet.
"It's that feeling that you just want to get back to work and put it to bed and put it right. We'll just have to make sure we keep that in the back of our minds [ahead of the next game against the Waratahs in Wollongong on March 6]."
Beaten after the hooter a week ago at home by the Highlanders after a bout of mumps swept through the team, the Brumbies were determined to hang on this time. "We did really well to hold them out," Brumbies captain Allan Alaalatoa said. "The boys were just holding on to that grudge from last week."
In other matches, the Stormers relied on unflinching defence — again — and a moment of magic from Springboks halfback Herschel Jantjies, to become the only unbeaten team left in Super Rugby.
The Cape Town-based Stormers beat the Jaguares 17-7 in wet weather to move three points clear at the top of the standings with four wins from four.
The Durban-based Sharks extended a two-year winning streak against the Melbourne Rebels after a 36-24 win.
In Brisbane, the Queensland Reds notched their biggest Super Rugby total, scoring 10 tries to thump Japan's Sunwolves 64-5.