It was the ninth straight win for New Zealand teams over their Australian counterparts.
Samisoni Taukei'aho scored for the Chiefs after just four minutes, a Luke Jacobson double giving the home team a 19-5 lead at halftime after Len Ikitau provided the Brumbies' only points in the first 40 minutes.
Damian McKenzie and Alex Nankivell crossed inside the first 10 minutes after the restart, while Anton Lienert-Brown's 64th minute try wrapped up a dominant performance.
For the Brumbies, Bayley Kuenzle scored just before the 60-minute mark, then Rob Valetini dotted down for an 80th minute consolation try.
In the earlier match, the Blues proved too strong for the Waratahs, finishing strongly for a 48-21 win at Eden Park after holding a tenuous 22-14 half-time lead.
Bryce Heem scored a hat-trick of tries as the Blues earned a bonus point and inflicted a record 10th straight loss on the error-prone Waratahs.
The Blues, as expected, took command in the early stages and opened up a 15-point lead by the 29th minute thanks to tries from Bryce Heem and Tom Robinson.
But Angus Bell burst through the home side's defence to reduce the deficit before Jake Gordon anticipated Finlay Christie's pass to steal possession and reduce the Blues' lead to a point.
Kurt Eklund's try three minutes before the break restored some breathing space for the Blues at the interval when he pushed his way over the line from close range.
Rieko Ioane scored with an opportunist's effort before a penalty try gave the Blues a 22-point lead, which was trimmed when Tahs hooker Dave Porecki drove across the line despite the Waratahs being down to 14 men following Harry Johnson-Holmes' sin-binning.
However, Heem slid across the line with 12 minutes to go to secure the bonus point before scoring his third try on the break two minutes from time to put the seal on the result.