The three points didn't come easy for the Brumbies, who were stretched to the limit by the Bulls.
Both sides were fighting for their seasons, having recently surrendered the lead in their respective conferences, and were ready to put up a fight.
Christian Lealiifano missed two early chances to open the Brumbies' account with a wayward pair of penalty goal attempts inside the opening 10 minutes.
His opposite number had no such issues, Hendre Pollard easily slotting a long three-pointer to take the lead after 17 minutes.
He got another moments later to go 6-0 up, as the Bulls heaped the pressure on at the breakdown.
The Brumbies couldn't break through the visitor's solid defence and efforts to test their lineout proved fruitless early on.
The situation only got worse when they lost Carter following an accidental but sickening knock to the knee by Bjorn Basson in the 23rd minute.
Heavily strapped and with the help of medics, the lock limped off and did not return.
But that only fired up the Brumbies, with a penalty and try to Carter's replacement Jordan Smiler - his first in Super Rugby - giving them an 8-6 buffer going into the break.
The Bulls regained the lead after an early second-half penalty goal, but a flying Henry Speight ensured that was only short-lived with two tries back-to-back - both converted by Lealiifano.
They could do nothing but watch, though, as the Bulls' scored from a rolling maul moments later to reduce the 22-9 deficit to 22-16.
Despite a few late efforts from the South Africans, the Brumbies managed to hold on for the win.
"It was a difficult game for us," said Brumbies coach Stephen Larkham.
"I think losing Sam Carter in that first half made it really hard with the changes in the forward pack, but I thought we handled it quite well in the second half."
Larkham wasn't sure how bad Carter's injury was and didn't want to pre-empt the results of scans on Saturday.
"He's in a brace at the moment," he said.
"It doesn't look like good news at this stage but we'll wait and see what the scans reveal."
Captain Stephen Moore lauded his side's defensive effort and the Brumbies' reserves, who held things together despite some confusion following Carter's departure.
"I thought our desperation was pretty good there in the end," Moore said.
"And at this point of the season we just need to win, and we found a way to do that tonight."
Bulls coach Frans Ludeke said Speight's brace - his third in Super Rugby - proved the turning point and leaves his side's finals chances at the behest of their rivals.
"Until the last whistle of the last game, you still hope," he said.
"But we need some favours from other sides."
- AAP
