The Brumbies withstood an early Lions attack, winger Shane Williams coming within a metre of scoring in his return Lions match before being bundled into touch.
The home side then worked their way out of danger, Mogg spreading a kick return wide to Andrew Smith, who drew two defenders before putting centres partner Tevita Kuridrani into the clear.
The Fijian-born flyer then made a mockery of the final two defenders, using young English winger Christian Wade as an impromptu shield against fullback Rob Kearney to open the scoring in the fifth minute.
The Brumbies missed three opportunities to extend their lead with one missed conversion and two missed penalties, before Mogg kicked a penalty from 45 metres out to extend their lead to 8-0 in the 39th minute.
Both sides then traded two penalty shots each, before the Lions made four changes in the 57th minute, the substitution of Englishman Owen Farrell for Hogg having significant impact.
Farrell steadied the directionless Lions and the results were immediate, the replacement No.10 knocking over two penalty goals to reduce the deficit to 14-12 in the 72nd minute.
But it wasn't enough, the Brumbies holding out to become the first side Australian provincial outfit to beat the Lions since 1971.
Brumbies coach White said the Wallabies would take confidence from the win.
"To get a win against the Lions - it doesn't happen. Even the Brumbies in their heyday couldn't do it," he said.
"I've been lucky enough to win a junior and senior World Cup. But to beat the Lions. It's as high as it gets."
Brumbies captain Peter Kimlin, who was a standout in the upset, said he could take knowledge of the win back into Wallabies camp.
"We went in there with a pretty clear mindset. We just wanted to keep it simple, hard workrate and big defence," he said.
Lions coach Warren Gatland said he felt his side didn't have the intensity required in the first half.
"Not the easiest conditions tonight, the Brumbies were really effective with what they did," he said.
"They didn't play any rugby, they just kicked a lot of the ball and competed really hard at the breakdown and tried to frustrate us and were successful."
Gatland added the win may be the wake-up call the Lions needed before the Test opener against the Wallabies in Brisbane on June 22.
Lions captain Rory Best said his side was smashed at the breakdown.
"They put pressure on us and our confidence started to go," he said.
"We lacked that little bit of composure."
- AAP
