Each time New Zealand conceded in the half, they recovered to frustrate the Americans with a disciplined defensive performance, so they will be annoyed to have missed out on a point.
The USA's opener came in the ninth minute from Carli Lloyd's header, but it will be the second that the Ferns will be more frustrated by. Sloppy defending enabled Alex Morgan, who was making her seventh Olympics cap, to score just after 40 seconds of the second half.
New Zealand had a series of half chances, but in truth, they never worried the American keeper Hope Solo and the result will leave questions for their manager Tony Readings.
Lloyd opens thcoring
The Americans had a great chance to open the scoring in the fifth minute from a Tobin Heath corner which was flicked on at the near post to Carli Lloyd, but her shot was stopped by Erin Nayler's reaction save.
Moments later, Heath's free-kick picked out Alex Morgan but the striker could only head over.
But in the ninth minute, the USA took the lead. Heath cut inside and whipped a delightful cross to Lloyd who headed the ball back across goal, finding the far corner.
New Zealand's first chance of note came in the 23rd minute from a long-range free-kick after Lloyd had fouled Ali Riley, however, Katie Duncan's effort went wide of the right post.
Hannah Wilkinson managed to get a shot on target just before the half-hour mark, but her effort was well held by Hope Solo.
Just before half-time, the USA could have made it 2-0 from Megan Kilingenberg's deep cross which found Morgan Brian, but she could only head wide.
New Zealand start second half poorly
New Zealand would have been proud at half-time about how they had frustrated the Americans after they had taken the lead, but that pride went out of the window straight in the second half as the USA doubled their lead after 40 seconds. Heath had broken into the box, but just before she could pull the trigger, she was tackled. But the Black Ferns could not fully clear and a simple pass from Brian found Morgan unmarked in the box, and she beat Nayler at the near post who should have done better.
New Zealand had a half-chance to pull a goal back from a Duncan free-kick that eventually fell to Amber Hearn, but she could only shoot narrowly wide of the left post.
The terrific Heath nearly found herself on the scoresheet when the ball fell to her on the edge of the box after a quick attack, but she could only shoot over.
Heath caused all sorts of difficulties from a free-kick on the right-wing as she whipped the ball into the corridor of uncertainty, forcing Nayler to make a parry and the New Zealand defence managed to scramble the ball clear.
New Zealand's late chances
As the game wore on, New Zealand was having more of an attacking threat. A Kirsty Yallop corner was initially cleared but Sarah Gregorious worked the ball back into the box where the ball looked like it would fall kindly for Hearn, but she was denied by a stunning clearance by Lloyd.
From a second corner, the ball was cleared to Rebekah Stott who tried her luck from distance and whilst her shot went narrowly wide of the far post, Solo never looked concerned.
But late on, the USA nearly scored their third. Great work from the substitute Crystal Dunn made room on the right and she drove a tempting ball into the six-yard box towards Heath who was only denied by brave keeping from Nayler.