The Pumas scored four tries to three to notch just their third-ever win over New Zealand, with 39-year-old hooker Creevy putting Argentina in front when he crossed late in the game to hand All Blacks coach Scott Robertson his first defeat.
Robertson's tenure opened with two tense home wins over England last month but they couldn't hold out against a committed Pumas side who trailed 20-15 at half-time.
Argentina won the physical exchanges in the second half, their forward pack superbly led by flanker and captain Pablo Matera.
Fly-half Santiago Carreras kept the scoreboard ticking over, landing seven of eight shots at goal for an 18-point haul, including a penalty in the dying minutes to extend Argentina's lead to eight points and seal a famous victory.
All Blacks fly-half Damian McKenzie kicked 15 points and set up two tries but his side were guilty of too many mistakes against opponents who feasted on errors.
It continues a nightmare run of results for the All Blacks at Wellington's Sky Stadium venue, where they haven't won any of their last five Tests, dating back to 2018.
They began well enough, with McKenzie landing an early penalty before he set up a sweeping try to lock Sam Darry through an audacious chip 10m from his own tryline.
Lucio Cinti responded with a try for Argentina after midfield partner Santiago Chocobares sliced through the defence on the halfway line.
McKenzie and Carreras traded penalties before McKenzie's deft pass put Waikato Chiefs team-mate Anton Lienert-Brown outside a defender to score.
Winger Mateo Carreras lifted the Pumas within five points on the stroke of half-time, pouncing when a high kick was batted back loosely by the All Blacks to dart over.
Argentina snatched the lead two minutes after the interval when lock Franco Molina powered over from a lineout drive for his first Test try.
Winger Mark Tele'a crossed to put the All Blacks 30-25 ahead nearing the final quarter.
But Argentina finished the stronger, with Test centurion Creevy powering over next to the posts in one of the highlights of his 18-year career with the Pumas.
The teams meet again in Auckland next Saturday.
