As his vehicle was spinning out of control due to the maneuver, Stephens pulled out a pistol and shot himself in the head.
Stephens was found dead as a result of a self-inflicted gunshot wound after being spotted by police in Western Pennsylvania, officials say.
Cleveland man Steve Stephens posted a video of himself killing 74-year-old Robert Godwin Sr., who was picking up aluminum cans on Sunday after spending Easter with his family.
At a Silicon Valley conference Tuesday afternoon, Facebook CEO Mark Zuckerberg briefly mentioned the Cleveland case.
Sheriff Fletcher said that once the connection was made, all deputies were put on alert and they had pictures of Stephens and his vehicle in their cars to keep an eye out for him to assist in his apprehension.
Mrs Wheeler said she heard sirens speeding past her "two seconds later" and described how police cars pursued the white Ford Fusion down the highway.
Federal partners were involved in the hunt for Stephens, and were stationed in Erie.
The shooting marked the latest video clip of a violent crime to turn up on Facebook, raising questions about how the world's biggest social media network moderates content.
WICU reports that Stephens went to a McDonald's drive-thru and ordered chicken nuggets and french fries.
After recognizing Stephens, the worker was able to give authorities extra response time by delaying his order.
In the video, Stephens told Godwin the name of his girlfriend and said, "She's the reason that this is about to happen to you".
Stephens was placed on the FBI's most wanted list and attracted a $50,000 bounty for information leading to his arrest.
Zuckerberg, speaking at Facebook's annual conference for software developers, expressed the sympathy of company employees to the friends and family of the shooting victim. "Period", Cleveland's police chief said.
"I am pretty sure he figured out that we were on to him", said DuCharme Jr.