BRISBANE – The Chiefs led the Reds 31-0 just after half-time but two Samu Kerevi tries meant they needed a Samisoni Taukei'aho try in the fifth minute of stoppage time to claim a 36-12 win and the bonus point.
It was the 35th straight win by New Zealand teams over Australian opposition and leaves the Reds in fourth spot in the Australian conference.
The Chiefs lost fly-half dynamo Damian McKenzie with a head knock midway through the first half but were always in command of the Brisbane game, scoring five tries to two.
"We were really stoked to get that bonus point right there at the end but it was very tough. It would have been nice to kick on after that first 25 minutes," Chiefs skipper Sam Kane said.
Veteran open-side flanker George Smith made his first appearance of the season for the Reds as a substitute after December back surgery.
The result completed a dismal 24 hours for Australian rugby after the Waratahs were held scoreless for the first time in a 29-0 loss to South Africa's Golden Lions in Sydney on Friday.