Brumbies centre Tevita Kuidrani scored the only try of the game in the fourth minute and Jesse Mogg landed three penalties for the hosts.
The Lions responded with two penalties for Stuart Hogg, who also struck the posts twice, and two penalties for his replacement Owen Farrell.
Ben Youngs was the only Tigers player to start the fixture, the Lions’ last game before the three-match Test series against Australia kicks off this Saturday.
His Tigers teammates Dan Cole and Geoff Parling came off the bench and helped to add impetus to the Lions’ in the final 20 minutes as the pack won two penalties for Farrell to cut the deficit to 14-12 with nine minutes remaining.
But the Lions were unable to create any more opportunities as the Brumbies held on to became the first provincial team to beat the Lions since Northern Transvaal triumphed 35-30 on 7 June, 1997. And the Brumbies also became the first Australian provincial team to beat the Lions since Queensland in 1971.