Highlanders coach Jamie Joseph admitted his side went off its game in the middle period but was still good enough to get the win.
Joseph said the Highlanders did play well enough to win the match but he acknowledged an excellent performance from the Brumbies.
"I thought the Brumbies played really well and put us under a lot of pressure.
"So it was pleasing to get the win in that context and I thought we played well," he said.
"The thing about this team is that we have to play to our absolute best to win games and that is what we did for the majority of the match. But in the middle period we tried to push passes and did the little things wrong."
Joseph said the side would take credit in winning what was a close game but it was vital the team stayed ahead during the match.
"We're the sort of team which probably can't chase games, so we have to stay in front.
"I can't compare to what had happened in the past as I wasn't here, but I know it is good for the team to win these close games.
"This is a big win for us, We never lacked for any belief for this game and were up for it. We've got another hard physical game next week, so that will set us in good stead."
Highlanders first five-eighth Colin Slade had a disappointing return to the field, being forced off early in the second half with a groin injury.
Joseph said Slade was obviously down but he hoped the injury was only short term.
Hooker Jason Rutledge, who helped himself for two tries in the victory, said the side probably did not get enough ball in the right area of the field but the side defended well.
The hooker scored his first try, running up the sideline to pick up a Jimmy Cowan chip and just a minute later was over in the other corner, up in support after a backline break.
"I couldn't concentrate after that as I was laughing so much," Rutledge said.
He said it was good to get a close win and the team would have been annoyed to have lost the match.
"If we had let that game get away from us it would have been pretty hard to get up for next week.
"It's always good to come home here and win.
"We've managed to win a few games down here over the past few years."
