But Hickey and Ma'a Nonu made errors from the kickoff to gift possession to the Chiefs and after good linking play from the Bay boys Sam Cane and Nathan Harris, man mountain Ben Tameifuna crashed over in the corner. Anscombe slotted the extras from touch to make it 7-7.
The Chiefs added the try of the half to Tim Nanai-Williams after 19 minutes from a long range sweeping movement as Blues fullback Charles Piutau lay prone on the ground with a match ending knee injury.
Anscombe's boot put the Chiefs up 17-7 before he and Hickey traded penalties to leave the Chiefs ahead 20-13 at the halftime break.
The early decisive points in the second half went to the Chiefs when Tameifuna crashed over for his second try after Tanerau Latimer went close to scoring.
Up 25-13, the match decider came in scintillating fashion after 50 minutes when under extreme pressure outside their own 22, the Chiefs shifted the ball cleverly to give Nanai-Williams space to bolt clear and set up Tom Marshall for an outstanding counter attacking try.
The Blues kept trying down 32-13 and scored a smart try of their own to George Moala with Nanai-Williams in the sin bin, but the Chiefs held out comfortably enough for a crucial victory.
Blues captain Keven Mealamu, in typically honest form, summed up the feeling immediately after the game.
"We played a bloody good side and that is why they are the champions at the moment."
Chiefs 32 (Ben Tameifuna 2, Tim Nanai-Williams, Tom Marshall tries; Gareth Anscombe 3 cons, 2 pens) Blues 20 (Lolagi Visinia, George Moala tries; Simon Hickey con, 2 pens; Ihaia West con). Halftime: 20-13.