The Canberra-based team scored four tries and dominated possession and territory in a commanding first-half display.
It was the Brumbies' seventh win in succession away from home, giving them the record for the most consecutive away wins in Super Rugby history.
It also left them undefeated this season and on top of the Super Rugby table with 23 points, six ahead of the Chiefs.
"We are extremely happy," captain Ben Mowen said in a television interview after the game. "It is not an easy place to come and win, and to pick up a bonus point is an absolute bonus.
"We knew against the Sharks you have to be extremely physical. We spoke in the week about winning those early moments and we are pretty happy with the way we did that."
Former Springboks coach Jake White has engineered an incredible turnaround in fortunes for the Brumbies since taking over midway through last season.
Their powerful forwards - a key feature of any White team - intelligent use of the ball, and excellent hand skills helped them race into a 26-3 lead at halftime against a Sharks side that had no answer.
The visitors had their first try inside five minutes, when quick hands from Christian Lealiifano set fullback Jesse Mogg over in the corner.
Joe Tomane added a second try before Matt Toomua went over after more quick ball off the floor left the Sharks exposed and unable to retreat in a defensive line.
By the time Henry Speight scored the bonus-point try five minutes before halftime, the Sharks had barely ventured into the visitors' 22.
There were boos from the Kings Park faithful directed at their own players as the teams went off at the break, but the home side had been outclassed in one of the best 40 minutes of Super Rugby seen from any side at the ground in years.
"In the first half we had no ball and were very passive in our defence," Sharks captain Keegan Daniel said.
"They had a lot of continuity and we just couldn't keep up. All the hard work from them was done in the first half and we couldn't play catch-up rugby."
The second half was less dramatic, but by then the hard work had been done by the Australian team.
Sharks loose forward Ryan Kankowski did barge his way over for a try, the first for his team in three matches, but it could not spark a comeback.