Captain Abby Erceg, along with fellow Northlander Hannah Wilkinson, put in strong performances.
They showed plenty of character in the middle of the park with Katie Duncan and Annalie Longo at their industrious best.
But, for all their toil, they could not break down a determined USA defence.
The USA began the second half in the same way as they started the night - in goal-scoring fashion.
American forward Alex Morgan, who has hurt the New Zealand team on a number of occasions, found space inside the penalty box and hammered a low shot past Erin Nayler at her near post.
Morgan continued her red-hot form in 2016 by netting her 12th goal of the year and fifth in Olympic play.
Throughout the 90 minutes, New Zealand did not create a clear goal-scoring opportunity but Hearn did have a sight of the target in turning and volleying wide five minutes after the break.
With goal difference likely to prove crucial in determining which countries make it past the group stages, it was vital for the Kiwis to make it through additional time unscathed and they did just that to post a two-goal defeat.
They will now look to bounce back on Sunday morning (NZ time) when they face World No. 24 Colombia, who play their opening game against France later today, at the same venue.