Scrumhalf Nic White scored their only try and Christian Lealiifano kicked five penalties as the Brumbies bounced back with a win after consecutive defeats to the Crusaders and Waratahs.
The Australian Conference leaders success was built on tactical kicking which pinned the Blues back for the majority of the first half, with the home side guilty of numerous handling errors and struggling at the lineout.
The Blues improved after the break but they gave themselves too much to do with the conditions not helping their exciting backline while much of the second half was spent resetting scrums.
"To come out here and play in the conditions like they were in the first half and execute our plan I thought our guys were really good tonight," Brumbies skipper Ben Mowen said in a pitchside interview.
"Our defence was extremely strong in that first half."
Lealiifano slotted two penalties in the first 17 minutes at Eden Park to put the Brumbies ahead 6-0 before White cleverly used the wet conditions to score the game's opening try five minutes later.
Blues winger George Moala dropped a greasy high ball and after the Brumbies forwards piled in to the ruck, the ball squirted free and White hacked through and slid over from well short of the tryline to avoid a tackle for the first five pointer.
Lealiifano failed to convert the tricky effort from near the right touchline but did slot another penalty before the hooter as the Brumbies went in 14-0 ahead at halftime.
Blues coach John Kirwan was seen angrily remonstrating with his team during the break and the tongue lashing drew some positive reaction with home team improving in the second period.
Flyhalf Chris Noakes slotted an early penalty to get them on the board before outside centre Rene Ranger crossed for a try in the 53rd minute after a smart dummy and break by All Black scrumhalf Piri Weepu.
Noakes converted to close the gap to 14-10 but Lealiifano slotted two more penalties to one from Blues replacement Baden Kerr as the Brumbies claimed the four points.
"Tonight, we gave ourselves an uppercut for the first half," a dejected Blues lock and skipper Ali Williams said. (Compiled by Patrick Johnston; Editing by John O'Brien)