Brumbies captain Ben Mowen said he was proud of his charges as they saw off the Chiefs to book their place in next week's Super Rugby semi-finals.
Mowen's men won 32-30 in Canberra, with four tries being scored by both side in an entertaining 80 minutes of knockout rugby the hosts won.
The Brumbies now wait to see whether they will travel to Sydney to face the Waratahs or head to Christchurch to tackle the in-form Crusaders.
"We knew it was going to have to be a full 80-minute performance, you just cannot knock a side like that over easily," explained the number eight.
"We're very proud of that effort and you've got to give the Chiefs a lot credit on what they've done over the last three years. It's been an outstanding effort to be there."
"We've been working hard on our skills not only over the last few weeks but probably over the last couple of months, getting good transfer into the game and it's exciting to play," Mowen said.
"If we keep getting results like that you have to keep backing it."
Chiefs captain Aaron Cruden added: "We started pretty slowly and gave a quality side like the Brumbies a lead like that.
"We did really well to peg it back and showed a lot of character, but in these play-off games you need to be clinical for 80 minutes."