The Rebels jumped out to a 13-0 lead after Fijian wing Sefanaia Naivalu scored a try midway though the first half then defended strongly when the Brumbies launched their fight back.
The Brumbies, who are still second in the standings but under increasing pressure from the other Australian sides after losing their last two matches in a row, got on the scoreboard when their Fijian-born wing Henry Speight crashed over on the stroke of halftime.
Christian Leali'ifano landed a penalty in the second half to cut the margin to five points but neither side was able to score again on a wet and windy night at Canberra Stadium.
“We were pretty poor tonight, the breakdown was really disappointing for us,” Brumbies skipper Stephen Moore said in a televised interview.
“We made a lot of mistakes tonight, it was tough conditions but that's still no excuse.”
The Rebels currently sit in 11th place on the table, with four wins and four losses this season.
“We couldn't be happier,” said Rebels captain Scott Higginbotham. “It was pretty nerve wracking at the end but we came away with the win. The boys really stepped up.”
Original source: Rebels defeat injury-ravaged Brumbies