The Waratahs led by six points heading into the final quarter, but a 61st-minute try from Brumbies winger Henry Speight and a Jesse Mogg penalty eased the pressure, with the visitors' hard-working defence keeping the home side scoreless until the final whistle.
The result saw the Brumbies retain a five-point lead over the Queensland Reds in the race for the Australian conference.
The Canberra club should seal the title in the final round next week when they return home to face the lowly Blues.
Berrick Barnes was one of the few bright spots of a disappointing night for the Waratahs, setting up their first try, scored by barnstorming hooker Tatafu Polota-Nau with a quick tap from a penalty in the 31st minute.
However, the hosts were made to pay for indiscipline, and allowed three penalty goals that saw the Brumbies go in at halftime with a 9-5 lead.
Barnes span out of two tackles and collided with one of the upright posts before slamming the ball over the line in the 57th minute to put the Waratahs 13-9 in front.
The Brumbies responded four minutes later with fly-half Holmes hurling a long ball wide to Speight, who danced around a tackler on the right touchline and cantered over near the right corner.
Mogg, from 35 metres out on a tight angle, curled his penalty kick back just enough to give the hosts a four-point break in the 64th minute, defiantly defended by the Brumbies defence.
"It wasn't exactly the victory we were after... but there's quality across that (Waratahs) pack," Brumbies captain Ben Mowen said in a pitchside interview.
"I'm really proud of these guys, we keep breaking these hoodoos... I thought our defence was much improved from the week before.
"It's good now, because we can say one game (to go) and then finals."
The winners of each of the Australian, New Zealand and South Africa conferences automatically qualify for the playoffs of the southern hemisphere provincial competition, while the next best three in the overall standings also go through.
The Blues unleashed a three-try burst in the second half to beat an injury-ravaged Western Force 32-9 at Eden Park and boost their hopes of avoiding Super Rugby's wooden spoon.
Flanker Steven Luatua scored a try in the first-half and Charles Piutau, Ma'a Nonu and Luke Braid all crossed in quick succession in the second to secure the Blues their third win in the penultimate round of a dismal season.
The Blues' bonus-point victory from scoring four tries lifted them a point above Perth-based Force into third from the bottom of the standings.
Johannesburg-based Lions sit bottom of the southern hemisphere's provincial championship, seven points behind the Force with two matches to play.
The Blues took a 13-9 lead at the end of an uninspiring first half littered with handling errors and befitting of the teams' lowly standing.
The Blues had the edge in territory and Ma'a Nonu raised a brief burst of enthusiasm from the sparse crowd by driving toward the line in the 28th minute but was denied a try by video review.
Luatua burrowed over the line near the right-hand corner moments later, however, to put the Blues up 8-6 against the Force who lacked captain David Pocock and veteran lock Nathan Sharpe due to injury.
Blues fullback Piutau broke open the game 15 minutes after the break, touching down at the right corner again after taking a long pass from Nonu.
Nonu helped himself to his 100th first class try minutes later, cantering 10 metres to the line, with an off-load from substitute Peter Saili cutting the Force defence to ribbons.
Number eight Luke Braid joined the party with a fourth try 10 minutes from the whistle.
Force fly-half Ben Seymour slotted three penalties in the first half to score all of his side's points as the visitors were kept scoreless for the last 45 minutes and slumped to their 12th loss of the season.
Flyhalf Elton Jantjies succeeded with all seven of his kicks at goal to help the Lions to a 37-32 win over the Melbourne Rebels for just their third Super Rugby victory of the season.
They held on following a fantastic comeback by the Rebels who scored three second-half tries to turn a 24-7 deficit into a 32-27 lead at Ellis Park.
But replacement flanker Jaco Kriel charged down the blindside to score an equalising try, which Jantjies converted from the touchline. He then kicked a penalty on the final hooter to stretch the winning margin to five points.
The Stormers claimed top spot in the South African Super Rugby conference with a dour 13-6 win over the Cheetahs on Saturday.
The victory moved the Stormers to 62 points, eight ahead of the Bulls and Sharks, with one round of league matches to play.
The Cape Town-based team missed the chance to go top of the overall standings, however, as they failed to pick up a bonus-point for scoring four tries and are still one point behind leaders the Waikato Chiefs.
The match was played in cold and very wet conditions with both teams content to play a tactical kicking game in an effort to gain territory.
The safety first approach meant scoring opportunities were limited and it took 17 minutes before Stormers fly-half Peter Grant kicked a penalty for the first points of the contest.
The Cheetahs finally drew level with two minutes left in the half thanks to a close-range penalty from pivot Riaan Smit, which saw the teams go in at the break deadlocked at 3-3.
The Stormers dominated territory and possession at the start of the second half and their cause was given a boost when Cheetahs fullback Willie le Roux was yellow-carded, five minutes after the restart, for a professional foul.
Grant kicked the visitors ahead with his second successful penalty but the Cheetahs, despite being a man down, levelled again when Smit kicked a long-range penalty in the 53rd.
The Stormers injected some life into the match almost immediately from the restart when Grant put in a deft corner kick that was collected by fullback Gio Aplon who went over untouched for a converted try.
The Cheetahs were the more adventurous team in the last quarter, but a Stormers' defence which has conceded just 18 tries this season, the best in the competition, held firm to secure the victory.
"The win was important for us," said Stormers captain Jean de Villiers.
"The conditions today were terrible. You couldn't play much rugby and it was almost better not to have the ball. We have one match left and we are happy where we are."
"We put up a good fight and we were in it right to the end. The match could have gone either way but it is tough to lose," said Cheetahs captain Adriaan Strauss.