Auckland were on the brink of winning the match at home at Colin Maiden Park when entering the final over with three wickets in hand and requiring only five run for victory.
But lively seamer Frauenstein bowled Anaru Kitchen and Lance Shaw off successive deliveries before tailender Michael Bates was run out seeking the one run required from the final ball.
The exciting finish ensured that a sparkling century to Canterbury opener Michael Papps was not in vain.
The former international scored an impressive 122 off 138 balls to pilot Canterbury to 287 for seven, which Auckland should have overcome after skipper Scott Styris set them on track with 71 off 77 balls.
Auckland's batting depth was apparent as they overcame the early dismissals of Tim McIntosh and Lou Vincent with a stand of 87 for the third wicket between Reece Young and English import Ravi Bopara raising their hopes.
Bopara departed from an edge behind off Rob Nicol after scoring 53 off 51 balls and Young later followed him back to the pavilion for 47.
It was left to Styris and Gareth Hopkins to resurrect their ambitions with a fine stand of 93, which ended when Styris top edged a full toss from Chris Martin.
Hopkins and Colin de Grandomme were dismissed for 48 and 20 respectively in the 10th and last over from fast bowler Shane Bond, setting up a grandstand finish.
Earlier, Papps' eighth domestic one-day century, and his second this season, highlighted an impressive Canterbury scorecard that featured two important partnerships.
Once opener Nicol departed for a first ball duck against his former team, Papps partnered Peter Fulton, who made 47, in a stand of 82 for the second wicket then collaborated with Johann Myburgh as another 91 were added for the third.
Myburgh's share was 39 while Shanan Stewart then chipped in with 35, but the major kudos was rightfully reserved for Papps, who raced through the 90s when successive sixes over mid wicket off de Grandhomme saw him leap from 88 to 100 in two balls.
He was eventually dismissed after adding another 22 runs to his tally, having struck 11 fours and three sixes.
