The Chiefs had to work hard against a Waratahs side who fought hard but dropped to 1-4 for the season after a try from fly half Bryn Gatland and two from winger Emoni Narawa got the visitors across the line.
Despite failing to claim a bonus point, the Chiefs opened up a six-point lead over the Brumbies at the top of the standings with the reigning champion Crusaders lurking in third place a further two points back pending the weekend matches.
"It was a real arm-wrestle," Chiefs co-captain Sam Cane said.
"They put us under a lot of pressure and we ended up dropping a lot of pill. We had to work really hard for it tonight."
The Waratahs, who had a try on an intercept from skipper Jake Gordon and another through a rolling maul from former captain Michael Hooper, put in an impressive defensive performance to stay in the match until the last few minutes.
"I thought our effort tonight was fantastic," said Gordon. "We probably need to change a few things around our attack, we're getting ourselves into some good places but we're allowing them to get on board and slow things down."
The Canberra-based Brumbies had not beaten the Crusaders in their last 11 encounters, and not in Christchurch for 23 years, so resting five key Wallabies for the trip looked almost like a concession.
The Crusaders have been struggling with a lengthy injury list but wasted little time in getting winger Leicester Fainga'anuku across the line for the first of his two tries, taking his tally for season to six in four matches.
Even the visitors' much vaunted rolling maul failed to get them over the line just before half time and the Crusaders rubbed salt into the wound by executing their own catch-and-drive to send hooker Codie Taylor over for their third try.
Brumbies skipper Ryan Lonergan and flying winger Corey Toole crossed after the break but a home win never looked in doubt and a late try from Crusaders replacement Christian Lio-Willie killed off any hopes of a comeback.
"I think regardless of who turned up tonight, we knew the Brumbies were going to front up," said Crusaders captain Scott Barrett.
"I'm proud of our boys and our efforts. Early on in the season we've had a few tough lessons and we've really drilled down to what this team is good at."
