Pocock touched down three times in the first half, all off the back of rolling mauls, and also had a hand in the opening try by Henry Speight, slipping an inside pass to the Fijian-born winger.
The Highlanders were weakened by the absence of Ben Smith, Aaron Smith and Malakai Fekito, who were allowed the week off to comply with New Zealand's request to give All Black players some breaks ahead of this year's World Cup.
The Dunedin-based outfit were also missing a handful of players through injury and were instantly up against it when they fell 17-0 behind after just 14 minutes.
Lima Sopoaga banged over two penalties to get the visitors on the scoreboard but Pocock's second and third five-pointers and the unerring boot of Christian Leali'ifano saw the Brumbies go to the break leading 31-6.
With a 25-point lead and a bonus point already in the bag, the Brumbies took their foot off the gas in the second half, failing to add to their first-half haul and allowing the Highlanders to close the gap.
Shaun Treeby crashed over from close range shortly after the restart then replacement loose forward Dan Pryor scored to cut the deficit to 13 points with 22 minutes remaining but that was as close as it got.
"We really needed that win after two losses," Brumbies captain Stephen Moore said in a televised interview.
"We would have liked to have kicked on the second half but we knew they would come back into the game.
"Maybe we dropped off a little bit but overall it was a good performance."
(Writing by Julian Linden in Singapore; editing by Sudipto Ganguly)
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