Winger Mateo Carreras brought Felipe Contepomi’s Argentina to within five points at half-time when he pounced on a defensive error to touch down.
The Pumas moved into the lead for the first time two minutes into the second half when lock Franco Molina scored his first Test try by powering over following a line-out.
Wing Mark Telea restored the All Blacks’ five-point lead but fly-half Carreras’ penalty moved the Pumas to within two points.
Iconic forward Creevy, capped 109 times by his country, then burrowed over and Carreras converted to put the visitors five points ahead.
The three-time world champions scrambled for a response but they made too many errors and Carreras’ late penalty put Argentina out of sight.
The teams meet again in Auckland on 17 August.
