Auckland compiled 226 for eight off 50 overs and the visitors appeared on track to comfortably overhaul it before Peter Fulton, Chris Harris and Andy Ellis were all run out in the space of eight overs late in the chase.
However, captain Kruger van Wyk kept his head, striking the winning boundary with seven balls remaining as Canterbury reached 229 for seven.
Van Wyk was 27 and Brandon Hiini ended unbeaten with a lusty 16, the pair combining for a crucial stand of 25 when Canterbury appeared to have thrown victory away.
They were 163 for four and facing a manageable runs required rate when Fulton was caught short for 60.
Harris followed soon afterwards for 17 and Ellis for 14 as some tight bowling from Colin de Grandhomme began to cause headaches.
De Grandhomme took three for 38 off eight overs while Chris Martin was classy at the top of the innings, taking one for 31.
Auckland's innings was based on a 107-run fourth-wicket stand between hard-hitting newcomer Anaru Kitchen and Reece Young, while de Grandhomme smashed 38 off 31 balls at the death.
Kitchen top-scored with 69 off 104 balls while Young reached 43 off 82.
Former New Zealand pace bowler was sharp but expensive for Canterbury, taking two for 57 off 10 while Ellis and Ryan Burson both claimed three scalps.
Defeat means Auckland are the only team yet to register a point after two rounds of the State Shield.