The Chiefs ran in five tries to extend their unbeaten run against the Blues to 15 matches after a breathless Hamilton thriller on Saturday.
The Blues, looking to put together five straight wins for the first time since 2011, never gave up and the home side had to fight tooth and nail for the win after Ma'a Nonu crossed for his second try in the 78th minute.
Flanker Lachlan Boshier crossed for a brace of tries for the Chiefs, who also had scores from scrumhalf Brad Weber, hulking winger Ataata Moeakiola and Jesse Parete as they beat New Zealand opponents for the first time this season.
A five-pointer from fullback Melani Nanai and the first from evergreen centre Nonu kept the Blues in touch before a brilliant finish in the corner in the 66th minute from winger Rieko Ioane, his eighth try of the season, set up the late drama.