The Brumbies secured back-to-back home victories when they beat the Stormers 25-15 in Canberra on Saturday.
The victory for the Brumbies is their first over the Stormers since 2010.
The Brumbies outscored the Stormers by three tries to two as they had a penalty try awarded at the end of the match after the Stormers scrum disintegrated on their tryline.
Before the penalty try the Brumbies had been leading 18-15 largely thanks to Nic White's two penalties over Peter Grant's one successful penalty.
Winger Robbie Coleman scored two of the Brumbies three tries, but it was his second touchdown in the 62nd minute that gave the home side the edge in a tight match against the South Africans.
With the Brumbies clinging to a 13-10 lead, Coleman chased down a kick ahead by captain and number eight Ben Mowen.
Stormers winger Jacobus van Wyk appeared to have the kick covered and waited for it to trickle into touch, but Coleman kept running and somehow twisted his body and grounded the ball just inside the corner post for a crucial try.
The Brumbies hung on despite Stormers' substitute back Juan De Jongh crashing over for a 75th minute try to cut the deficit to three points.
Experienced fly-half Peter Grant missed a relatively easy conversion three minutes after hitting a post with a penalty attempt.
In a frantic last three minutes, Coleman was denied a hat-trick when the ball rolled out of play as he led the chase and then centre Pat McCabe was held up.
A penalty try from a scrum on the bell sealed the points for the Brumbies.
The Stormers were quicker to settle and Grant posted first points from a seventh-minute penalty after missing his first attempt three minutes earlier.
The Brumbies hit back in the ninth minute when fly-half Matt Toomua sliced through and set up Coleman for his opening try.
White's conversion put the Brumbies up 7-3, but the home team struggled to put together multi-phase moves, missed more tackles and gave away several breakdown penalties.
From one of the penalties, powerful Springboks number eight Duane Vermeulen powered his way over from close range after a drive from the Stormers pack following a lineout.
Grant's conversion gave the Stormers a 10-7 advantage before the Brumbies responded with two of their own to lead 13-10 at the break.
The win took the Brumbies above the NSW Waratahs at the top of the Australian conference, while the Cape Town-based Stormers are only above the Central Cheetahs in the South African conference after their third defeat on their Australasian tour.
"It's really tough to play the Stormers and it's a really nice result on the back of some good form over the last couple of weeks," Brumbies skipper Ben Mowen said.
"We knew they were going to play for their season after eyeing off at least two victories on their tour and they zeroed in on us."
Stormers captain Jean de Villiers said his team paid for a lack of composure near the end of the match.
"Not just the kickers but I thought the whole team made too many mistakes towards the end and I thought we lost our composure," de Villiers said.
"It doesn't get any easier and we play the Queensland Reds next week and we need to change a bit and learn from our mistakes."
Final Score Brumbies 25 (13) Stormers 15 (10)
Tries - R.Coleman 2, Penalty Try
Pen - N.White 2
Con - N.White 2
Tries - D. Vermeulen, J.de Jongh
Pen - P.Grant
Con - P.Grant
Cards - T. Liebenberg (30th min yellow)
Referee: Glen Jackson
Assistant Ref 1:James Leckie
Assistant Ref 2:Andrew Lees
TMO : Peter Marshall
1. JP Smith, 2. Stephen Moore, 3. Ben Alexander, 4. Scott Fardy, 5. Sam Carter, 6. Jordan Smiler, 7. Jarrad Butler, 8. Ben Mowen (c), 9. Nic White, 10. Matt Toomua, 11. Robbie Coleman , 12. Pat McCabe, 13. Andrew Smith, 14. Joe Tomane, 15. Jesse Mogg
Replacements: 16. Siliva Siliva, 17. Ruan Smith, 18. Ruaidhri Murphy, 19. Jack Whetton, 20. Lachlan McCaffrey, 21. Michael Dowsett, 22. Stephan Van Der Walt, 23. Lionel Cronje
15. Gio Aplon , 14. Kobus van Wyk , 13. Jean de Villiers (captain) , 12. Damian de Allende , 11. Sailosi Tagicakibau , 10. Peter Grant , 9. Nic Groom , 8. Duane Vermeulen , 7. Siya Kolisi , 6. Deon Fourie , 5. Michael Rhodes, 4. Ruan Botha , 3. Frans Malherbe , 2. Tiaan Liebenberg , 1. Steven Kitshoff
Replacements: , 16. Stephan Coetzee , 17. Oliver Kebble , 18. Brok Harris , 19.Jurie van Vuuren , 20. Nizaam Carr , 21. Louis Schreuder , 22. Demetri Catrakilis , 23. Juan de Jongh