A scything run and perfect pass from Tom Wright allowed Lachie Lonergan to score in the 79th minute, just two minutes after the Brumbies had given up the lead at GIO Stadium in Canberra.
The Force had dominated the first half before the Brumbies' big men took over in a 10-minute span, twice scoring from rolling-mauls to take the lead.
Having trailed 22-16, the Force looked to have pinched the points when Jake McIntyre crossed to score in the 77th minute, following a falling offload from Fergus Lee-Warner to put him through.
It was the 11th straight time the Brumbies have beaten the Force, a streak that dates back to 2013.
The Force carried the ball at a three-to-one ratio through the first half, but they failed to find the line, their three penalty goals seeing them trail 10-9 at the break.
Noah Lolesio's poise had created the game's first try, the Brumbies' star skipping around a Force opponent and delivering a perfect cut-out ball to Wright who surged over the line after 20 minutes.
Twice the Force were held up in goal, the best chance a diving run from Tim Anstee after he found space following a lineout set-piece, with only a desperate dive from Wright preventing the try.
While they had little possession, the Brumbies' outside backs always looked the more dangerous in open space and their pack strength earned a penalty on the stroke of halftime.
Force grabbed the lead straight after the break with Manasa Mataele and Toni Pulu combined to break through the middle drive them into attack, with the latter finding the corner to grab his side a 16-10 lead.
But the Brumbies immediately struck back through Folau Fainga'a, who stumbled over to score after his side's rolling maul drove them towards the line following a lineout deep in Force territory.
They doubled up minutes later in identical fashion, Scott the beneficiary of the unstoppable maul for a 22-16 advantage.
The Brumbies continued to search for the line after a string of penalties under the posts and opted against extending the margin, but the Force scrum stood up to prevent them finding an insurance try.
Second-half substitute Lonergan proved the match-winner, while Brumbies' skipper Allan Alalaatoa was man of the match for his breakdown dominance.
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