Joe Powell clinched the match when he ran 20m to score with eight minutes to go. His replacement, reserve halfback Matt Lucas, scored a try in the final minute.
"I'm really proud — the Sharks threw a lot at us and the way the boys kept digging deep for each other was special," Brumbies captain Christian Leali'ifano said. "The forwards have been amazing all year, they were challenged again and stepped up and provided a great platform for us."
The Jaguares are also in form, having won 10 of their past 11 games. The Brumbies' most recent loss came against the Argentine side in Buenos Aires eight weeks ago.
The Brumbies, who claimed Super 12 titles in 2001 and 2004, haven't played a final since 2013, when they lost to the Chiefs. The last Australian side to win was the following year when the Waratahs defeated the Crusaders in Sydney.
The Brumbies will go into Saturday's semifinal without Samu, who suffered a hamstring injury in the first of his two tries. Samu told rugby.com.au that he went into the quarter-final with a hamstring niggle.
"It's been tight throughout the week and it just tightened up that last bit of the first half. I didn't want to risk it," Samu said.
Blake Enever joined the Brumbies touring party as a replacement while they have depth in the back row with Locky McCaffrey and Jahrome Brown on the bench last weekend.
"We don't want to get overconfident but the boys definitely take some confidence out of the past seven weeks. That game is done now and we have to look to next week," Samu said. "We had a loss to them earlier in the season and they're definitely a quality side. The last thing we can do is focus on them.
"We just have to focus on ourselves and what we can control and hopefully heading over there, we just give it our all and hopefully get the result."
- Additional reporting AP
