Although they are still in a decent position, having gone into the game as the only unbeaten side in their pool, they will look back on this match as a missed opportunity.
They conceded two sloppy goals, forcing them to chase the game, and couldn't convert large periods of dominance.
The timing of the match might not have helped. Their first two games were played early in the morning and they have been following a sleep programme to make sure they are alert in the morning - but this one tipped off at 9.15pm local time, under a full moon often peeking out from behind the clouds at Riverbank Arena.
They started poorly and gifted Argentina their first goal inside the first five minutes when Kayla Sharland lost possession deep in her own half and Carla Rebecchi took advantage.
The Black Sticks eventually found some rhythm and pegged Argentina in their own half for large periods of the remainder of the half, even forcing three penalty corners in quick succession, but couldn't capitalise.
Stacey Finlayson created a great chance to score early in the second period but twice scuffed her shot and less than 30 seconds later New Zealand fell 2-0 behind when Rebecchi finished off a fast break.
They gave themselves a chance as the game opened up when Charlotte Harrison tapped in from close range but they also came under considerable pressure as they pushed numbers forward.
Group B is now condensed with four of the six teams on six points and New Zealand probably need a further four points from their two remaining pool games to guarantee a place in the semifinals.
They must beat the United States in their next match on Sunday morning to keep their medal chances alive before their final pool game against Germany.
New Zealand 1 (Charlotte Harrison 62) Argentina 2 (Carla Rebecchi 5, 45). HT: 0-1.
