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The victory earned the Brumbies, champions in 2001 and 2004, the long trip to Buenos Aires next Friday to play the Jaguares, who beat the Waikato Chiefs 21-16 in their quarter-final.
The Canterbury Crusaders, 38-14 winners over the Otago Highlanders, will take on the Wellington Hurricanes, who earlier beat South Africa's Bulls 35-28, in the other semi-final next Saturday.
On a chilly night in the Australian capital, number eight Pete Samu grabbed a brace and Henry Speight also crossed to give the Brumbies a 24-6 halftime lead with Joe Powell and Matt Lucas touching down in the last 10 minutes.
Centre Andre Esterhuizen crossed as the Sharks fought their way back into the contest in the second half but comeback wins in successive weeks proved beyond the travel-weary South Africans.
"The Sharks threw a lot at us at various times and the way the boys dug deep was really special," Brumbies captain Christian Lealiifano said.
"The way these boys have handled anything that's been thrown at them has been amazing. We know we've got a lot of travel ahead of us but we're in this part of the season and we're happy."
Efficient, well-organised and unexceptional in all but their rolling maul, the Brumbies have now put together a seven-match winning streak since they lost to the Jaguares in Argentina in April.
They flew out of the blocks against the Durban-based Sharks and a neat inside pass sent Samu cantering towards the line for his first try with less than a minute on the clock.
Winger Speight finished off another slick move sparked by a Tom Banks break in the 10th minute and flyhalf Lealiifano, who converted all five tries, slotted a penalty to extend the lead to 17-6 in the 21st minute.
Fullback Curwin Bosch had kept the visitors in touch with a couple of booming penalties but Samu secured his second try after 24 minutes off the catch-and-drive to give the Brumbies a comfortable lead.
There was no further score until 17 minutes into the second half when the Sharks drove their own maul towards the Brumbies line and the confusion allowed Esterhuizen to burst through tacklers to score.
The visitors were now dominating possession and they sniffed the chance of a last-gasp victory to match the one they secured with a try at the death against the Stormers in Cape Town last week to win a place in the playoffs.
It was not to be, however, and the Brumbies muscled up to keep the visitors out before Powell's solo effort sealed the win after 71 minutes with Lucas putting a gloss on the scoreline after another break from fullback Banks in the final seconds.
"Really good fight there in the second half," said Sharks skipper Louis Schreuder.
"We fought for the place in the playoffs last week but from our standards, not a good enough season."