Stephens's photo had gone up on billboards and more than 400 tips had poured in before the suspect was spotted in Pennsylvania.
That call led to a police pursuit which soon ended with Stephens killing himself, according to the Pennsylvania State Police.
Stephens' vehicle sustained minor damage after a trooper couldn't stop in time and hit the auto, but no other injuries to law enforcement were reported.
The chase lasted two miles before Stephens took his own life, police said.
Pennsylvania State Police said officers saw Stephens in Erie County on Tuesday morning.
A trooper slid into Stephens' vehicle, causing minor damage, but no one was injured, police said. They need to take this as a lesson.
During the almost 48 hours that Stephens was on the run, the American media gave nonstop attention to the case, particularly emphasizing the use of Facebook to make public the horrifying images of Godwin's execution-style killing.
Stephens posted the video on his Facebook profile page along with broadcasting a Facebook Live video explaining that he was going to kill other people.
He says the attendant recognized Stephens, who was wanted in Sunday's slaying of a retired OH man, and called 911.
In a statement early Monday, police warned residents of Pennsylvania, New York, Indiana and MI to be on the lookout for Stephens, who they said may have traveled out of state.
Detectives spoke with the suspect on Sunday by mobile phone and tried to persuade him to surrender, police said.
Police say Godwin is the only known victim.
A daughter of the Cleveland man killed in a video posted to Facebook wanted gunman Steve Stephens to die "in a hail of 100 bullets" - while other relatives hoped the crazed shooter would have faced justice. Video of the killing was uploaded to Facebook. State Police Maj. William Teper Jr. would say only that the tip came from a "concerned citizen".
She said the two had dated for a while and even looked at engagement rings at one point.
Stephens's mother told CNN she called him on Sunday after learning about the video, and he had told her he was shooting people because he was "mad with his girlfriend". "But we have to forgive him, because if we don't forgive him, the Bible says your Heavenly Father won't forgive you".
"We feel awful for the family of Mr. Godwin and their tragic loss", Nancy Kortemeyer told the Daily News. The woman, Joy Lane, told WJW-TV in Cleveland that she last talked with Stephens on Saturday night, when he told her he had quit his job and was moving out of state. A $50,000 reward is being offered for information leading to his capture and prosecution. Gillispie reported from Cleveland.