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The Reds largely dominated possession and territory on Friday night but had only six penalty goals - three from James Tuttle and three from Jono Lance - to show for it.
Fortunately, it was all they needed to secure their first victory of the new season, proving the Reds are made of much sterner stuff than what their season-opening defeat to the Melbourne Rebels suggested.
The Brumbies went over twice - through halfback Joe Powell in the first half and Isi Naisarani with five minutes to go.
Neither effort was converted, letting Queensland off the hook in front of 11,034 fans at Suncorp Stadium and handing Brad Thorn his first Super Rugby win as coach.
Lance sealed it with his third penalty in the dying minutes.
"Sometimes you appreciate a tougher game," Thorn said.
"It's not so attractive... but they're playing for each other and the jersey.
"That's the sort of thing I want to see. I just love seeing Queenslanders go at it."
Like last week, the Reds again were reduced to 14 men after Caleb Timu was yellow-carded controversially for a "cynical infringement" - a no-arms hit on Tom Banks - just before halftime.
But they came through it unscathed on the back of a performance built on ferocious defence and a strong set-piece showing.
The introduction of JP Smith - who replaced the injured James Slipper just before the break - helped cement their dominance with a series of crucial scrum penalty wins.
At least four golden opportunities to cross the line went begging for the Reds in the first half alone.
Powell helped nullify two of them, getting underneath Taniela Tupou to deny a certain try in the opening stages, before saving another 20 minutes later by knocking a loose carry out of Eto Nabuli's hands.
When Powell spotted a small gap in the Queensland line and darted through on 30 minutes - followed by Timu's sin-binning - it looked as if the jig was up.
But it only proved a false dawn for the Canberra side, who were left frustrated after pushing the Reds all the way.
"It came down to our inability to control possession," Brumbies coach Dan McKellar said.
"There's no excuses from us. We turned over ball at set piece, pushed the pass on occasion, simple dropped balls."