Trailing for most of a match that made up for a lack of quality with plenty of commitment, replacement Highlanders prop Aki Seiuli barrelled over under the posts in the 73rd minute for a converted try that proved to be the difference.
The Brumbies then set about utilising their favourite attacking ploy, the driving maul off a lineout, in a frantic finale, but the visitors held firm on three occasions to either draw a penalty or force a turnover to keep their lead intact.
The welcome win was just the second in five matches for the injury-depleted Highlanders, who will hope to build on the success with a couple of home fixtures looming in Dunedin. The Brumbies have now lost three of their five matches.
"I'm just really proud of the way that we defended at the end there. The Brumbies have got a great lineout and maul but we managed to shut them down so I am delighted we held on for the win," Highlanders captain Ben Smith said in an interview.
From the opening whistle, the Highlanders defence restricted Brumbies scrumhalf Joe Powell for both time and room, and looked to put pressure on the home side down the flanks with quick offloads to their dangerous backline runners.
The Brumbies were being starved of possession but still scored the first points of the match after 16 minutes when they finally put together a run of phases and flyhalf Wharenui Hawera kicked a long-range penalty following an infringement at a ruck.
The Highlanders were making too many handling errors to punish the hosts, who stretched further ahead after 27 minutes when loose forward Chris Alcock peeled off a maul and threw two clever dummies before strolling over in the corner.
Hawera kicked the conversion to make it 10-0 but the Highlanders battled back to half the deficit by the break when winger Sio Tomkinson put the finishing touches to a sweeping move from a scrum after several minutes of constant pressure.
Replacement Highlanders flyhalf Marty Banks traded penalties with Hawera early in the second half before he pulled the visitors to within two points from another kick in the 64th minute after a late hit on visiting scrumhalf Aaron Smith.
The decisive moment arrived nine minutes later when the Highlanders charged down a clearance deep in Brumbies territory and despite being held up over the line as they poured forward, Seiuli peeled off a five-metre scrum to score the winning try.