Tunkhannock Community Ambulance Association Chief Michael Henn identified the two survivors as Steven Gay and William Earnest, The Times-Tribune of Scranton reported.
The crash occurred near Skyhaven Airport in Tunkhannock, about 20 miles west of Scranton, Federal Aviation Administration spokesman Jim Peters said.
Gay's father, airport owner Charles Gay, said the pair were trying to reach an area designated for landing if a plane experiences problems.
"They made the first line of trees. They knew they wouldn't make the second line of trees so they ditched in the river," Henn said.
The single-engine plane landed upright but soon overturned in the river, leaving the men belted in their seats upside-down for a short time before they could free themselves, Henn said.
Steven Gay was teaching Earnest to fly, with the student at the controls, according to his father.
Charles Gay said he had taken off in a plane right behind the pair, and spotted them in the river when he did not see them in the air. He landed his plane to offer help.
One man was taken to Mercy Tyler Hospital, and the other refused treatment, officials said.
A nursing supervisor at the hospital said she could not provide any information on the patient.
An FAA inspector was on the way to the scene. It was not immediately clear if the National Transportation Safety Board would investigate.