Crystal Dunn beat a German defender in the area and squared a pass to Ohai, who sent a right-foot shot over goalkeeper Laura Benkarth in the 44th minute.
"I saw Crystal making a run and every time she does that you know she is going to get something in the box," Ohai said. "I sprinted as fast as I could and she got the ball to me and I just squared it."
Ohai's goal was the first given up by Germany in the tournament. The two teams met in the group stage, with Germany winning 3-0 on Aug. 27 in Miyagi.
"It was a great performance by our team," U.S. coach Steve Swanson said. "It's a reflection of a lot of people's efforts. We had some adversity in the group stage but the players learned from that and our character showed tonight."
Germany pressed forward for an equalizer after the break but the Americans defended staunchly to protect the lead. Leonie Maier rattled the crossbar from distance in the 72nd and came close again with a long-range shot in the final minute, but U.S. goalkeeper Bryane Heaberlin made a good save.
"Our defence got better and better as the tournament went on," Swanson said. "They deserve a lot of credit, and when I say that I include the goalkeeper. We needed to stay compact. We got a little stretched out against Germany in the first game against them so we knew we needed to be better defensively and that was a key to our winning tonight."
Germany scored 15 goals in the group stage, but just couldn't find a way to break through in the final.
"I don't think beating them 3-0 had any implications for today's match," Germany coach Maren Meinert said. "Playing the United States is always tough. We gave up a goal in the first half and that made it harder for the players to respond and it was a totally different situation than the first time we played them."
The U.S. also won this tournament in 2002 and 2008. Germany won in 2004 and 2010.
Earlier Saturday, Japan got goals from Yoko Tanaka and Asuka Nishikawa to beat Nigeria 2-1 and take third place. Desire Oparanozie scored for Nigeria.