Police say Stephens had a permit to carry a concealed weapon.
After a brief, 2-mile traffic pursuit, Stephens pulled out a handgun and killed himself, Reed said.
Police named a Cleveland man, Steve Stephens, as the primary suspect in the Sunday murder.
On Easter Sunday, Stephens posted a video to Facebook of his confrontation with Robert Godwin, 74, as he was walking home from a family Easter gathering.
In further alarming videos posted publicly, Stephens allegedly claimed to have killed 13 people and said himself to be "working on 14". "He wasn't moving so I panicked and started screaming and hollering", Driscoll said. Godwin seems confused and repeats the name and then Stephens says, "She's the reason this is about to happen to you".
The video of the killing was up for three hours before it was taken down, raising questions about Facebook's handling of objectionable material posted by its users.
Police would not speculate on what was behind the killing, but videos Stephens posted showed him talking about losing everything he had to gambling and trouble with his girlfriend.
One of Godwin's daughters, Debbie Godwin, said she wished Stephens had been captured.
Police Chief Calvin Williams says anyone who thinks they've seen Stephens should call 911. Facebook disabled Steven's account soon after it received complaints about the video. "But we know we need to do better", the company said in a statement. "I am sorry that all of this has happened".
She also said Stephens was "a nice guy" who was good to her and her children.
Authorities are offering a $50,000 reward for information that will lead to Stephen's arrest. But investigators believe there are not other victims. Police in Philadelphia said eight elementary schools and a high school were locked down Monday while they investigated reported sightings but found nothing.
"We have our closure in regards to our search for Steve Stephens", Cleveland Mayor Frank Jackson said.