It was an uncharacteristically mistake-ridden display from the Highlanders, who went into the match following victories over the Stormers, Crusaders and Blues. Wing Waisake Naholo, the competition's top try-scorer with seven, had been a key factor in their form, but he was very quiet in Canberra, the ball hardly going to him and when it did he was often on the back foot.
To compound matters for the Highlanders, lock Joe Wheeler went off with a knee strain which could put him in doubt for next weekend's home match against the Sharks.
The victory will be a welcome boost for the Brumbies, who have endured a horror past couple of weeks. They followed up their lacklustre loss to the Blues at Eden Park with a poor defeat at home to the Rebels, the first time the Melbourne-based team have won in Canberra.
Pocock was a force in the first half, as his three tries testify, but they could be concerned at the way they struggled to break down the Highlanders after the break, particularly following Wheeler's injury which left them a man down and vulnerable. Instead, it was the Highlanders who finished stronger.
Brumbies: 31 (David Pocock 3, Henry Speight tries; Christian Lealiifano 4 cons, pen)
Highlanders: 18 ( Shaun Treeby, Dan Pryor tries; Lima Sopoago con, 2 pens)
HT: 31-6