Owens caught up with one of the men, who turned around and shot the officer in the stomach just beneath his bulletproof vest, Stacho said. Owens returned fire and the suspect then exchanged shots with Owens' partner.
No one else appeared to be injured, Stacho said.
Owens underwent surgery at MetroHealth Medical Center but died early Saturday, a hospital spokeswoman said.
Police arrested one man in the shooting but no charges had been filed, Stacho said. Investigators returned to the east-side neighborhood Saturday to collect more evidence, he said.
Police had received complaints from residents about the neighborhood, where many boarded-up duplexes had been vandalized. Owens was a 10-year veteran of the police department.