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.