Providing they get past Scotland in the final game of pool play they should secure a semifinal berth.
Having seen South Africa go down 19-21 to England in their pool, the New Zealanders have a chance to steal a march in the championship standings on their rivals.
Tim Mikkelson, who scored the try that secured the game for the All Blacks Sevens said: "We circled this one and pretty much said if we don't win this one we won't be playing tomorrow. It's a massive effort for the boys, they started very well and the bench came on and finished it.
Captain Scott Curry said with some of their best players back they knew the United States would be stronger than they were in the series opener in Dubai.
"They played really well right to the end there. We've got to recover well and one more game against Scotland tomorrow," he said.
He was aware of Scotland's threat as they had looked sharp in their games in the tournament.
An early penalty against Perry Baker for holding onto the ball as Tone Ng Shiu attempted to turn over the ball provided the All Blacks Sevens with their first chance.
From the tap the All Blacks Sevens moved the ball and it was Ng Shiu who fed Scott Curry into a lovely gap and he ran in from 40m for the opening try.
New Zealand turned the ball over with an intercept just out from the United States line, and from a tackle penalty, the USA moved the ball and when it reached Baker's hands on the left flank there was no one to match his speed as he scored unchallenged.
Ng Shiu was in the action again with an inside pass to Kurt Baker which split the American line and allowed the senior player to run 60m and score and with the conversion to give New Zealand a 14-5 lead at the turn.
Having conceded two penalties in potential scoring situations, New Zealand secured the game moments after Tim Mikkelson had taken the field as a substitute, he disturbed an American lineout throw, secured the ball and powered his way 30m downfield to score the match-winning try with two minutes remaining.
Sam Dickson capped the effort with the final try after foundation work put in by Etene Nanai-Seturo in the final moments to secure the win.
Earlier, New Zealand started strongly with a seven-try 47-0 win over Wales in their opening game. Tim Mikkelson scored tries either side of Regan Ware's second minute try with Joe Webber, Scott Curry, Kurt Baker and Vilimoni Koroi all touching down afterwards. New Zealand led 28-0 at halftime.
Ngarohi McGarvey-Black completed the try scoring by landing five conversions with Koroi adding another.