Morgan scored in the 22nd minute and Ohai added hers in the 70th for their first goals of the tournament and gave the Americans some revenge after being eliminated by the Nigerians two years ago in the quarterfinals.
The United States will face the Germans on Saturday in the title match, seeking a third crown in the six tries. It also will look to avenge a 3-0 loss to Germany in the first round, the only game it has been held without a goal.
Nigeria had the first chance when Francisca Ordega beat onrushing U.S. goalkeeper Bryane Heaberkub to the ball but pushed her attempt wide of the post.
But an unmarked Morgan put the Americans ahead when she redirected Mollie Pathman's cross past Nigerian keeper Ibubeleye Whyte at the back post. It was only the second goal scored in the first half of a game in the tournament by the United States.
The Americans, which conceded the possession advantage to Nigeria in the game, had a chance to double its advantage in the first half but Kelly Cobb's header went just over the crossbar.
An apparently equalizing goal for Nigeria by Desire Oparanozie in the 52nd minute was negated by offside and the Americans capitalized but adding an insurance tally 18 minutes later. Second-half substitutes Chioma Ubogagu and Samantha Mewis combined to feed Ohai, whose shot was deflected by Whyte but continued into the net.