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The side coached by Argentine Mauricio Pochettino secured qualification thanks to goals from Folarin Balogun (45) and Malik Tillman (82).
The co-hosts, staging the World Cup alongside Mexico and Canada, completed the match with 10 players after Balogun was shown a straight red card in the 64th minute.
Balogun became the first player to score and be sent off in a World Cup match since France's Zinedine Zidane in the 2006 final against Italy.
The United States will face Belgium, who beat Senegal 3-2 after extra time (2-2 after normal time), in the last 16 in the US city of Seattle next Monday.