The Chiefs are now undefeated in their last 14 games against the Blues, which is the longest unbeaten streak for any team against another in Super Rugby history, but they were behind for much of the match before securing their hard-fought success.
The Chiefs came from a 14-19 half-time deficit to win when referee Paul Williams awarded a penalty try in the 74th minute as the home scrum powered towards the line against a battling Blues side, down to 14 men.
"We didn't finish our chances but what was pleasing we didn't get frustrated and we kept our composure in the last 15-20 minutes," said Chiefs captain Sam Cane at the final whistle.
The Chiefs scored the game's first try after 12 minutes through wing Sean Wainui after a series of smart passes from Damian McKenzie to go 8-6 up but the boot of flyhalf Stephen Perofeta kept the Blues in the contest.
Blues captain James Parsons scored just before half-time, with the try awarded after consultation with the Television Match Official, to give the visitors a 16-14 lead, extended immediately after the break by another Perofeta penalty.
The Chiefs turned up the pressure in the final stages with Blues lock John Goodhue being sent to the sin bin just before the final 10 minutes, effectively handing the home side the advantage they needed to regain the lead and go on to win.
The Blues, beaten 64-40 at home by the Sharks last week, have now lost five of their six games in the 2018 campaign and remain bottom of the New Zealand standings.