The chase lasted 2 miles before Stephens shot himself in the head after the vehicle spun and came to a stop, police said.
The family of Robert Godwin, the 74-year-old man killed Sunday while walking on a Cleveland sidewalk, spoke with CNN's Don Lemon just hours before his killer, Steve Stephens, shot and killed himself, Tuesday morning.
As police approached, Stephens killed himself.
"This started with one tragedy and ended with another person taking their own life", said Cleveland police chief Calvin Williams. Video of the killing was uploaded to Facebook.
Stevens was spotted by a worker at a McDonald's drive-thru near Erie, Pa., police said.
At the Tuesday conference in California, Facebook founder and Dobbs Ferry native Mark Zuckerberg expressed his condolences to the family of a Cleveland man whose death was posted on the social media site on Easter.
One of Mr Godwin's daughters, Debbie Godwin, said she wished Stephens had been captured.
Facebook said Stephens' account was suspended within 23 minutes of the murder video being reported, but admitted it needs to "do better". "She's the reason that this is about to happen to you,"Stephens reportedly said".
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The video, which was posted on Sunday by OH man Steve Stephens, showed the graphic murder of 74-year-old Robert Godwin Sr.
The murder and a video sparked outrage across the world and renewed scrutiny of the growing number of grisly videos being posted on social media.
WICU reports that Stephens went to a McDonald's drive-thru and ordered chicken nuggets and french fries.
After a brief exchange in which Mr Godwin was asked to say a woman's name - that of Stephens' ex-girlfriend, Joy Lane - he was shot dead.
Stephens is believed to have videotaped his actions and published it on Facebook, along with another video threatening to kill others and claiming he had already killed 13 people.
Police later located him by a cellphone ping.
A $50,000 reward was offered in this case, and many people are urging authorities to give the money to the McDonald's employee.