Prop James Slipper celebrated his 200th appearance in the competition with a try while Charlie Cale scored twice and hooker Liam Bowron crossed the line eight minutes from time to launch a late flurry that killed hopes of a Crusaders comeback.
Flanker Rob Valetini's try with two minutes remaining and a breakaway by hooker Corey Toole earned Stephen Larkham's team a bonus point to see them join New South Wales Waratahs at the top of the standings with 10 points from the opening two rounds.
"We wanted to put an effort in that would get us a result and we were up for the game," said Slipper.
"I thought the boys did really well today and it's a special occasion for the lads.
"Most Aussie teams come here and put up the fight but never get the chocolates, so to come away with the result, and the way it ended up, it's a big result for us."
The Brumbies moved level with Australian rivals the Waratahs, who picked up their second win in a row with a 36-13 victory over the Fijian Drua on Friday with winger Max Jorgensen scoring a pair of tries in Sydney.
Replacement hooker Ioane Moananu also scored two tries for Dan McKellar's side with flanker Charlie Gamble and lock Angus Blyth crossing the line.
Waikato Chiefs sit in third in the standings on eight points following a 26-23 win over the Otago Highlanders, with hooker Samisoni Taukei'aho scoring two tries. But it was Leroy Carter who crossed for the most eye-catching try of the weekend.
The centre touched down in the 32nd minute after team mate Quinn Tupaea caught the Highlanders napping with a quickly taken lineout drop out that allowed him to race down the touchline before offloading for Carter to score.
Auckland Blues, meanwhile, secured their first success of the new campaign with a 42-32 victory over hosts Western Force as fly-half Stephen Perofeta claimed 17 points, including converting all six of his side's tries.
Wellington Hurricanes romped to a 52-10 win over Moana Pasifika in the New Zealanders' season-opener, with winger Josh Moorby scoring a hat-trick of tries while centre Fehi Fineanganofo and Number 8 Brayden Iose crossed the line twice.
Moana had taken a sixth-minute lead through a fine individual effort by winger Tuna Tuitama but were soon overwhelmed by the home side, who opened up a 19-point advantage by halftime and extended that lead throughout the second half.
"They started well, they whacked us on the nose but we recovered quite well and it's a pleasing enough performance," said Hurricanes centre Jordie Barrett. "We're never going to be perfect, it's round one for us."