Both teams came close to a winner in the last 10 minutes, with goal keeper Stefan Marinovic twice coming to the rescue of the New Zealand side with top saves.
The All Whites performance wasn't always as polished as the game against Mexico, as they struggled to defend both flanks and captain Winston Reid was forced to intervene on numerous occasions.
But the visitors showed tremendous resilience to come back into the match, after the home side had dominated the first half.
The Americans, who were on a nine game winning streak in Washington D.C., opened the scoring in the 31st minute.
It looked a soft goal, as American winger Green beat Marinovic at his near post with a snap shot from just outside the penalty area.
Marinovic has been impressive since coming into the side two years ago, but seemed to freeze as the ball flashed past him.
Defenders Andrew Durante and Liam Graham also won't enjoy the replay, as both defenders were guilty of hanging off the Bayern Munich forward before his snapshot.
That moment changed the momentum of the first half, as the United States took control.
The All Whites had moments where they threatened, usually through the power of Wood or the energy of Patterson, but spent most of the rest of the half trying to win back possession.
Both coaches made a raft of changes in the second half, and the game began to lose some shape. But the All Whites pushed until the end, in an all-out search for an equalizer rather than settling for a draw.
United States 1 (J Green)
New Zealand 1 (M Patterson)
Halftime: 1-0
