Bottom of the New Zealand conference, the Blues had tries from Matt Duffie, Akira Ioane and Melani Nanai but kept the home side try-less to clinch their fourth win of the season.
The Brumbies slumped to their sixth loss and third in succession but remain top of the weak Australian conference, with their lead trimmed after the second-placed New South Wales Waratahs beat the Queensland Reds on Saturday.
None of Australia's five teams have registered a win over New Zealand opponents this season and while the Brumbies battled hard, they never truly threatened Tana Umaga's Blues.
Needing a converted try to win after the final hooter, they went through a dozen phases in a desperate push towards the Blues' line but it all came to nought when captain Sam Carter fumbled a pass.
"It's massive, we know how proud the Brumbies are," said Blues captain James Parsons. "I'm proud of the boys' resilience."
The Blues were the livelier side early on and the Brumbies spent much of the opening half camped in their 22, repelling wave after wave of attacks.
In-form Blues winger Duffie was rewarded in the 31st minute when scrumhalf Augustine Pulu floated a long pass out wide to crack open the defensive line.
Centre George Moala was caught by a tackler near the right corner but offloaded inside to Duffie who shot an arm out to plant the ball on the line.
The Brumbies missed a chance to hit back six minutes later when scrumhalf Joe Powell released Tom Banks in midfield but the fullback delivered poorly inside to winger Henry Speight and the try chance went begging.
Banks left another five points on the field, fumbling a pass when steaming over the try-line on the stroke of halftime.
Carter waved away a shot at goal after the hooter to go for the try off the catch-and-drive but the Blues killed the rolling maul to go into the break with an 8-3 lead.
The Brumbies rallied, drawing within a point after two penalties from flyhalf Wharenui Hawera but were soon on the back foot when number eight Ioane rumbled over in the 55th minute from a rolling maul.
Replacement back Nanai pushed the lead to 18-12 with the Blues' third try 12 minutes from time and the New Zealanders defended stoutly to secure the win.
(Reporting by Ian Ransom in Melbourne; Editing by Nick Mulvenney)
