Green converted a first-half penalty and added goals in the 61st and 71st minutes, leaving the United States with four points, just behind North Korea on goal difference in Group B and one point ahead of France. Earlier Tuesday, North Korea and France played to a 1-1 draw. Two teams will advance.
The Americans had nearly twice the possession as the African debutantes and outshot Gambia 26-4. However, it needed Green's penalty in the 25th - created when left back Brittany Bassinger was brought down as she sent a cross into the box - to take the lead.
Green, who was the leading scorer at the CONCACAF championship in May with 12 goals, then had two more as the Americans scored five in the second half.
Amber Munerlyn coverted a feed from Darian Jenkins to double the lead 35 seconds into the second half before Green added another when her shot from the right side deflected in off Gambian defender Amy Jaju.
Jenkins also was instrumental in Green's third before Morgan Stanton and Toni Payne completed the scoring in the 83rd and 86th.
The six goals topped the Americans' previous high at the World Cup, eclipsing its 4-2 victory over South Korea in the 2008 quarterfinals.