The Australian side had looked set to fall foul of the deadly boot of Morne Steyn as they trailed by four points with two minutes to go, but Tevita Kuridrani's try saw them off.
Christian Lealiifano then added further gloss with the conversion, with the kicker having gone head-to-head with Steyn throughout in an enthralling shoot-out.
They will now have the chance to go for a third Super Rugby title and, short of a wobbly period in the second half, it was hard to argue against the merit of their victory.
For the Bulls, a constant insistence on turning down penalties in the last quarter in favour of running the ball cost them.
The Brumbies could not have hoped for a better start as they got some early territory and, when the Bulls stormed in from the side, Lealiifano had a simple penalty to kick things off with three minutes gone.
The same man then missed another three-pointer but that was soon forgotten as his men scored an 11th-minute try.
With the Bulls deep in their own half they were cut open by Henry Speight who put up a pass for Jesse Mogg and he did the rest. Lealiifano added the two.
The Bulls had a chance to chip away at the 10-point deficit when Steyn lined up a penalty after an offence by Clyde Rathbone, but he was off the money.
South African points would come, though, and with 15 minutes gone JJ Engelbrecht walked over the top of Speight and dotted down, with Steyn again awry with the boot.
He would find his range in the 21st minute, however, nailing a penalty which was washed out by one from Lealiifano.
Steyn responded with another penalty but when Lealiifano replied once more for his side, it meant the visitors took a 16-11 lead into the break.
The see-saw nature of the scoring continued into the second half as Steyn struck another penalty to reduce the gap to two points - something which remained as the hour-mark approached as he and fellow point-scorer Lealiifano traded further three-pointers to 19-17.
With his earlier misses now forgotten, Steyn then nosed his side ahead for the first time with another penalty.
Steyn then added a further penalty which, with five minutes to go, gave his side a four-point cushion which looked invaluable.
It was ultimately surmountable, though, and Kuridrani took a ball from Matt Touma to strip away and score, with Lealiifano adding the extras.
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