Despite being last in the New Zealand group, the Blues were too good for the conference-topping Brumbies in a stark illustration of the gulf between Kiwi outfits and their trans-Tasman rivals.
It was the Brumbies' third loss in a row and ninth consecutive defeat to New Zealand opposition.
The Blues dominated possession from the outset on Sunday but were unable to breach the Brumbies dogged defence for the opening half hour in front of 12,072 at GIO Stadium.
Winger Matt Duffie broke the deadlock, with a George Moala offload helping him to cross after 31 minutes.
Brumbies fullback Tom Banks also showed glimpses in attack, but was unable to hurt the Blues on the scoreboard.
Brumbies captain Sam Carter's decision to back their rolling maul to score a try rather than give Wharenui Hawera a penalty goal attempt on half-time did not pay dividends and the Blues went to the break leading 8-3.
Hawera got a chance three minutes into the second half and kicked well, shaving the deficit to two.
He put the home side in front with his third penalty after 51 minutes, but it did not take the Blues long to regain the lead and a well-worked lineout allowed Akira Ioane to drive over for a try and make it 13-8.
Bryn Gatland missed the conversion and the Brumbies began to apply pressure on the Blues defence.
That culminated in Hawera's fourth goal bringing them within one point with 20 minutes remaining.
As momentum shifted back to the Blues, they were able to capitalise on their opportunities with a Melani Nanai try coming from a scrum, setting up a match- winning lead and helping his side to pick up a crucial bonus-point victory.