Chiefs wingers James Lowe and Tom Marshall scored the tries as the twice winners picked up their sixth win in eight matches to stay in touch with the unbeaten Wellington Hurricanes at the top of the standings.
The winless Blues, though, remain rooted to the foot of the table after their seventh defeat of the season. Their losing run of nine, including two losses to finish the 2014 campaign, only intensifies the pressure on head coach John Kirwan.
The visitors had looked like ending the barren run after they led 13-10 with 20 minutes to go but Marshall broke through a tired defence to score the crucial try in the 68th minute after several phases of play beginning deep in Chiefs territory.
The Blues had fallen 10-0 behind after 30 minutes when Lowe ducked under the Blues tacklers to score the first try after taking a neat reverse pass by skipper Liam Messam.
But the Chiefs, without All Black centre Sonny Bill Williams who was a late withdrawal with an unspecified problem, were guilty of failing to convert the bulk of possession into points.
Dan Bowden kicked a penalty before the break to send the Blues in 10-3 down and the flyhalf then found himself booting the visitors level in the 48th minute after Jerome Kaino's try, the skipper and number eight powering over from the back of a five-metre scrum despite desperate attempts to halt him.
Bowden then slotted his second penalty five minutes later as the Blues sensed a momentum shift but Aaron Cruden levelled things up with a three-pointer of his own before Marshall's try.
Cruden added another penalty with six minutes to go but Ihaia West's reply on the buzzer ensured at least a losing bonus point for Kirwan's side in their second loss of the season to the Chiefs.
Original source: Auckland's blues continue as Chiefs win