It is the first time the New Zealand men's team have lost to the United States.
The USA scored on the stroke of fulltime, before nailing the sideline drop kick conversion to snatch victory from the jaws of defeat.
New Zealand earlier beat France and Portugal, before losing to the Americans.
New Zealand, France and the USA all finished the group stage on 7 points but New Zealand top the pool due to their superior points differential.
New Zealand will play Samoa in tonight's quarter-finals.