The men stopped at a convenience store in Washington, where they were spotted, Hewett said.
They fled and crashed into a fence near 24th Avenue SW and Lindsey Street, where officers captured Chase Clemons, 21, the sheriff said.
Taylor Brotherton, 28, fled on foot. Clemons told officers Brotherton had a handgun.
“As a precaution, we are locking down all of our schools while the NPD works this non-school-related incident with an armed suspect in our community,” said Shelly Hickman, spokeswoman for Norman Public Schools.
The two inmates were serving time for drug charges, Undersheriff Bill Shobe said.