Winger Emoni Narawa has scored two first-half tries as the Chiefs extended their winning start to the Super Rugby Pacific season to six matches with a 20-13 win over the Blues.
The Chiefs' 6-0 start is a record for the club and, having beaten the Blues, includes wins over both of last year's finalists.
Narawa scored his first try only 26 seconds into the match and added a second as the Chiefs took a 17-10 lead to halftime.
The Chiefs held out the Blues in a second half in which both teams managed only a penalty goal.
The Blues were attacking hard at the end, hoping to score a converted try to take the match to extra time.
But winger Caleb Clarke, a try-scorer earlier, knocked on in the last play of the game and the Chiefs held out to win.
"It was good to (score) about 30 seconds in which was a great start," Chiefs captain Brad Weber said.
"We owed these guys one after last year. They embarrassed us on our home turf so you could see the desperation in the defence in the second half.
"That was what that was all about."
All Blacks five-eighth Beauden Barrett had one of his worst matches with muffed goal kicks, handling errors, tactical mistakes and poor general kicking which cost the Blues in a tight match.
"We always know it's going to be a big job coming down here," Blues captain Dalton Papali'i said.
"Every game against these guys is a Test match. The boys prepared well but we just didn't execute some moments out there and it cost us."
Chiefs 20 (Emoni Narawa 2 tries 1min, 26min; Damian McKenzie 2 pens, 2 cons), Blues 13 (Ricky Riccitelli try 9min, Caleb Clarke try 17min; Beauden Barrett pen). HT: 17-10.
CHIEFS (1-15): Ollie Norris, Samisoni Taukei'aho, John Ryan, Brodie Retallick, Tupou Vaa'i, Samipeni Finau, Sam Cane (co-c), Luke Jacobson, Brad Weber (co-c), Damian McKenzie, Etene Nanai-Seturo, Rameka Poihipi, Daniel Rona, Emoni Narawa, Shaun Stevenson
RESERVES: Tyrone Thompson, Aidan Ross, George Dyer, Naitoa Ah Kuoi, Pita Gus Sowakula, Cortez Ratima, Bryn Gatland, Liam Coombes-Fabling
BLUES (1-15): Jordan Lay, Ricky Riccitelli, Nepo Laulala, Cameron Suafoa, Sam Darry, Anton Segner, Dalton Papalii (c), Hoskins Sotutu, Finlay Christie, Beauden Barrett, Caleb Clarke, Harry Plummer, Rieko Ioane, AJ Lam, Stephen Perofeta
RESERVES: Kurt Eklund, Ofa Tuungafasi, James Lay, Patrick Tuipulotu, Tom Robinson, Sam Nock, Corey Evans, Jacob Ratumaitavuki-Kneepkens/Zarn Sullivan
Referee: Angus Gardner
Assistant Referees: Ben O'Keeffe, Marcus Playle