A gallant Blues side came close to stopping the Chiefs’ winning run, going down 23-29 at Hamilton Stadium.
The Blues led 20-10 early in the second half and 20-15 with 30 minutes remaining.
But the Chiefs fought their way back into the game with two tries to regain the ascendancy.
All Black Brodie Retallick charged his way over to give the Chiefs a 29-20 advantage until an Ihaia West penalty on fulltime gave the Blues a deserved bonus point.
The Blues played with most of the ball and territory especially in the first half, and if they had taken all their chances like the Chiefs did, then the result may well have been different.
The home side were forced into counter-attack and capitalised on turnovers but there was much to admire from the effort of the Blues who continue to improve game by game in a match of excitement, speed and massive collisions.
There were two changes to the Blues line-up with Melani Nanai replacing Lolagi Visinia who was injured in training on Thursday while a fit Jerome Kaino responded well to his first full week of training from his shoulder injury to be included.
The Blues managed to dominate possession and territory for much of the first half. The clear difference was that the Chiefs were potent and clinical with their few chances while the Blues missed two clear chances.
They made an early bust through Ihaia West through the middle only for the ball to be passed outside to the marked Blake Gibson with Bryn Hall in clear air on the inside.
Immediately the Chiefs made ground on a counter attack after collecting a dink kick over the advancing defence with ultimately prop Mitchell graham powering over in the corner.
The Blues pushed back on to attack, moving the ball with width and depth from side to side with Nanai given clear space but was brought down by Damian McKenzie from behind. From the resulting rick Piers Francis suffered a neck injury and was replaced by George Moala.
West slotted a penalty to keep the Blues include but after more prolonged attack, the home side broke out, taking advantage of a missed tackle in the middle of the park with Shaun Stevenson converting the overlap.
The Blues again pushed back on to attack and were rewarded with a latte penalty to finish the half in touch at 10-6 down.
There were plenty of outstanding contributors with the pack again splendid at set piece with captain James Parsons outstanding with Steven Luatua and Blake Gibson prominent and in the second half replacement Akira Ioane gave plenty of go-forward ball.
The breaks came on the outsides with Nanai and Rieko Ioane dangerous and Rene Ranger made some telling breaks.
The only significant injury was with Piers Francis with a neck injury that was not serious.
Blues 23 (Melani Nanai, Rieko Ioane tries; Ihaia West 2 pen, 3 con)
Chiefs 29 (Mitchell Graham, Aaron Cruden, Seta Tamanivalu, Shaun Stevenson, Brodie Retallick tries tries, Damian Mckenzie 2 con)