Curtis Allgier, whose wears a swastika and the words "skin head" on his heavily tattooed face, fired a shot in the Arby's that hit no one before a customer at the restaurant snatched the gun, Salt Lake City police Sgt. Rich Brede said.
"It sounds like he was heroic, even though he's being humble about it," he said of the 59-year-old customer, who didn't want to be identified.
Allgier, 27, was captured in an office and taken to jail to await charges.
Allgier got the gun from corrections officer Stephen Anderson while he was in an examination room at the University of Utah orthopedic center awaiting an MRI for back pain around 7:45 a.m., university Police Chief Scott Folsom said.
The procedure requires an officer to replace metal restraints with a plastic "flex cuff," said Tom Patterson, director of the Utah Department of Corrections.
"There was some kind of altercation inside an exam room, the suspect got control apparently of the officer's weapon, fired at the officer, striking him at least once. The officer has succumbed to those injuries," Folsom told CBS Station KUTV.
Anderson, 60, a 22-year-veteran, was shot in the head, authorities said.
"This is one of the risks in the job we perform for the community," Patterson said. "Unfortunately the risk sometimes is our very lives."
Allgier forced two people out of a Ford Explorer outside the med center, Brede said; neither was hurt.
Officers chased the SUV at speeds up to 100 mph. Two Salt Lake City squad cars crashed into each other while trying to cut off Allgier, Brede said, but there were no serious injuries.
Allgier's friend, Trisha Tower, said he called her while on the run to say he had shot an officer and was sorry.
"I didn't even know how to deal with that," she said at her Salt Lake City home.
Police pursuing Allgier placed tire spikes on Interstate 215, but he still was able to drive several miles before bailing out in the Arby's drive-thru lane, police said.
Police arrived at the eatery just as Shirley Smiley, 57, was outside after breakfast with her husband and son. She said she heard a "popping noise" from inside, and police yelled "Get down!"
About six other customers and three employees were inside the restaurant, Smiley said. At least one person was "struck with some object" but was able to walk out, bloodied around the head, Brede said.
Allgier had been at the Utah State Prison in the Salt Lake City suburb of Draper on a parole violation. On June 14, he was sentenced to nearly nine years in federal prison for being a felon in possession of a firearm but had not been transferred yet to the U.S. Bureau of Prisons.
The university serves as a regional medical center for Utah and has two hospitals and other facilities, including the orthopedic center. The corrections department routinely transports prisoners there for medical appointments.
It was not clear whether Allgier had a lawyer yet, and an attorney who represented in a recent federal criminal case did not immediately return a call seeking comment.