Aso touched down in the seventh minute and grabbed two more in the second half as the defending champions mowed down a 21-14 deficit at half-time at McLean Park to win their seventh game from eight in the season.
Callum Gibbins collected a brace of tries in the second half, with Cory Jane, Mark Abbott and Ngani Laumape also crossing.
Tevita Kuridrani, Sam Carter and Joe Powell scored tries for the Brumbies who were kept scoreless for the final 50 minutes of the match.
The Hurricanes' Barrett brothers were relentless in the eight-try rout, with All Blacks flyhalf Beauden pulling the strings and fullback Jordie slotting all seven of his conversion kicks.
Replacement back Otere Black converted Laumape's final try to keep the kicking record perfect.
Brumbies flyhalf Wharenui Hawera also slotted all three of his conversion kicks but was responsible for a howling error that sparked a late onslaught that took the game away from the visitors.
Attempting to clear from deep in defence with his team trailing 28-21, Hawera's kick was charged down to allow Gibbins to swoop on the ball and charge over.
The floodgates opened, with TJ Perenara's quick hands putting lock Abbott through a hole near the line four minutes later, opening a 40-21 lead that the Brumbies had no hope of clawing back.
The Hurricanes' win continued Australian teams' winless streak in the competition against New Zealand sides.
The Brumbies slumped to their fifth loss of the season but still hold onto top spot in the Australian conference.
(Reporting by Ian Ransom in Melbourne; Editing by Sudipto Ganguly)
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