New Zealand had the better of the opening exchanges but for the first time in the tournament failed to open the scoring. In the fourth minute a rare mistake from Stacey Michelsen in midfield saw her forgo possession and Germany forced a penalty corner.
They made a hash of their first attempt but when the Black Sticks failed to clear Nina Hasselmann netted from close range.
If that was bad, even more crucially, the defenders decided to use their team referral to appeal the goal, despite Hager clearly yelling from the dugout not to. It has been a feature of this tournament so far, that the defensive unit, perhaps because of their youth, tend to be trigger happy with appealing.
Almost immediately, New Zealand were in penalty trouble again. They conceded two penalty corners in succession, with the Germans scoring from the second, only to have it annulled by the video referee for obstruction.
Still, the New Zealand defence seemed all at sea and when they cleared straight to a German attacker, found themselves in penalty trouble again in just the ninth minute. In a carbon copy of their first, Nina Hasselmann swept home from near the post.
There was some doubt over the awarding of that corner but New Zealand were unlucky to have Chinese umpire Lin Mao officiating at their end. Perhaps it is a lack of feel for the game, perhaps it is the sun visor she insists on wearing, even at night, that obstructs her view but the Chinese official has so far been the least competent official at the tournament.
While there were some half chances to the Black Sticks, it was no surprise when the Germans scored their third goal in the 20th minute and from Hager's point of view surely the worst of the lot.
The Germans cut them open up the middle and the energetic Lisa Hahn, who has been one of the best performers in this tournament, slotted home at the far post.
New Zealand created chances before the break - with Clarissa Eshuis hitting the post from a penalty corner - but Germany looked more dangerous. The Black Sticks were always under pressure in possession.
Germany was always one step ahead while the Black Sticks were plagued by poor passing, often of the 'hit and hope' variety. No one wanted to take the initiative and it showed in a disjointed, flat display.
After a stern halftime address, New Zealand lifted the tempo, accuracy and talk in the second half and their effort in pressing the German defenders was particularly impressive.
They put together some of their best passing movements of the tournament so far and were unlucky not to create more than a couple of half chances, though it was always going to be difficult as Germany often had the entire team in the defensive third.
Their efforts were finally rewarded in the 60th minute, when Anita Punt slashed home a rebound from the edge of the circle.
In the day's earlier matches, Great Britain beat China 3-1 while the Netherlands disposed of the hapless Japanese 4-1 (Argentina will play Korea in the final pool match.)
New Zealand 1 (A. Punt) Germany 3 (N. Hasselmann 2, L. Hahn)
Halftime: 3-0
Herald on Sunday writer Michael Burgess travelled to Argentina with assistance from Hockey NZ.