Scrumhalf TJ Perenara and replacement winger Matt Proctor also scored for the home side, who are still mourning the death of former All Blacks and Hurricanes loose forward Jerry Collins earlier this month following a car crash in France.
Flyhalf Christian Lealiifano (two) and fullback Jesse Mogg slotted penalties for the visitors, who could do little to shut down the high-octane attack from the home side.
The Hurricanes will host next week's final against the winner of the match later on Saturday between the 2014 champions the New South Wales Waratahs and Otago Highlanders.
"It's massive for us," skipper Conrad Smith said of the home advantage in a pitchside interview.
"It was a big motivation for us to know that if we kicked one in tonight we would play here, so it's a big edge for us.
"But I just loved our intensity tonight."
Renowned for his bone-jarring tackles, Collins would have been proud of his former team as they withstood a torrid opening five minutes from the visitors and then, as they have done so consistently all season, simply got into their work.
The pack took the ball forward and committed defenders before the backline, sparked by new All Blacks winger Nehe Milner-Skudder, made breaks out wide.
That relentless pressure eventually told and winger Julian Savea was able to barrel over to open the scoring in the 21st minute before Perenara then finished off another break from Milner-Skudder for his 11th try of the season.
Beauden Barrett converted to give the Hurricanes a 12-0 lead that was cut to 12-3 when Mogg landed his penalty after the halftime hooter had sounded.
Openside flanker Ardie Savea crashed over shortly after the break from a rolling maul to give the home side a 19-3 cushion.
Lealiifano then kicked two penalties to drag the Brumbies back into the game before the Hurricanes seized control of the contest for the final quarter with Proctor scoring their fourth try with seven minutes remaining.
"It's a shame to come so far and not get the result tonight," said Brumbies flanker David Pocock.
"But credit to the Hurricanes, they showed why they're the best team in the competition this year. Clinical in attack and their defence forced errors at crucial moments."
Original source: Hurricanes send Brumbies packing