Goalkeeper Bryane Heaberline recorded her third straight shutout and the Americans avenged a 3-0 loss to Germany in the group stage. Germany had won all five previous games in the tournament without allowing a goal.
Ohai scored in the 44th minute, finishing a sprinting run down the right sideline from Crystal Dunn.
Dunn worked past Annabel Jaeger and served a low ball back into the middle of the area where Ohai volleyed from near the penalty spot.
Germany had its chances to equalize, but Heaberline deflected Leonie Maier's effort off the crossbar with 15 minutes remaining and denied Lina Magull in the 89th.
The victory adds to the crowns won by the Americans at the initial World Cup - then an under-19 event - in 2002 and again in 2008.
The title comes a little over a month after the United States won the Olympic women's gold medal at the London Olympics.