Substitute forward Luke Reimer capitalised on his team's one-man advantage to score a decisive late try in Dunedin on Friday night, lifting the Australian side to third in the standings.
The result came as a relief for Larkham, whose team led the competition through the opening weeks before they lost three of their last four games.
"We had to sort of stay in it, keep composed and wait for our opportunity," Larkham told reporters.
"Things didn't go our way, but we kept our composure and that's probably a trait of the team that we've seen this year.
"It's putting us in a really good position to win these sorts of games."
Captain Ryan Lonergan scored the opening try in his 100th match for the Brumbies and landed both conversions.
Trailing 7-3 at halftime, the Highlanders went ahead through wing Jona Nareki's try.
A late yellow card shown to Highlanders hooker Henry Bell for high contact helped pave the way for the Brumbies to launch a late attack which resulted in Reimer's try.
Seasoned scrum-half Lonergan believed the result could mark a turning point in their season.
"We started really well and then we let ourselves down in a few games so to be able to grind this one out, it's massive for us," he said.
"It's still not exactly how we want to play our game."
Larkham surprisingly replaced back-rower Charlie Cale midway through the first half, for what he said was "tactical reasons".
Cale has been among the best players in the competition, scoring a league-leading nine tries.
The Brumbies face the Fijian Drua next week while the Highlanders, whose fifth defeat leaves them in eighth place, will play the Auckland Blues.