"We landed with our wheels pointed to the sky," Jared Litroff, 15, of Woodcliff Lake, N.J., told The Salt Lake Tribune.
Brooke Garber, 16, of Miami, said the "slow-motion" rollover was terrifying. "Everyone just started kicking out windows," Garber said.
The tour bus was carrying 47 teenagers and seven adult staffers on a six-week tour of the American West, said Jeff Gass, director of Rein Teen Tours of Wayne, N.J.
Gass said the teenagers - from Connecticut, Florida, New Jersey, New York, Philadelphia and other places on the East Coast - were to travel Friday to a hotel in Flagstaff, Ariz., aboard another bus.
"It's amazing - we were very lucky from a terribly unfortunate incident that everybody walked away with minor cuts and bruises.
The trip remains intact, and we're working as well as we can to get back to normalcy," Gass told The Associated Press on Friday.
The bus was operated by Arrow Stage Lines of Nebraska. Arrow was the owner of another tour bus that crashed near Mexican Hat, Utah, in January, killing nine Phoenix-area skiers returning from a trip to Telluride, Colo.
The company referred questions to a Lincoln, Neb., lawyer who was unavailable on Friday.
Utah Highway Patrol spokesman Cameron Roden said Arrow's driver was cited for drifting out of his lane before plunging into the dry creek bed. The driver's name wasn't immediately available.
Speed may have been a factor, Roden said, but investigators have yet to establish how fast the bus was traveling on winding state Route 12 through Red Canyon, a gateway to the national park, 220 miles south of Salt Lake City.
"It was a miracle nobody was hurt," Alberto Vasquez, administrator of Garfield Memorial Hospital in Panguitch, said Friday.
"They are doing fine now. The community had a barbecue for them after they were discharged. we brought clothes from a little boutique and thrift store in town," he said. The teenagers' belongings burned on the bus.
"Girls were screaming and crying," Derek Barocas, 16, of Long Island, N.Y., told The Salt Lake Tribune. "Others cried they were bleeding and that the bus was on fire."
The occupants made it out of the bus and onto a hill just in time to watch flames fully engulf the bus, he said.
Early Friday, Bridget Ann Serchak, a spokeswoman for the National Transportation Safety Board, said she was trying to determine whether her agency planned to investigate the bus crash.