Owens was executed at the Broad River Correctional Institute in Columbia, South Carolina, on Friday evening.
He was pronounced dead at 18:55 local time (22:55 GMT) after being injected with a drug called pentobarbital. He made no final statement.
His death followed a pause in executions in the state because prison officials were unable to procure the drug required for lethal injections.
Owens was sentenced to death in 1999, two years after killing Graves, after being convicted of murder, armed robbery and criminal conspiracy.
The day after he was found guilty, he killed his cellmate in jail, reports CNN affiliate WHNS.
According to reporting on his trial by South Carolina newspaper The State, Owens was 19 when he and Steve Golden, then 18, held Graves at gunpoint while attempting to rob the convenience store where she worked.
Owens shot and killed Graves after she failed to open a safe below the counter, according to testimony provided by Golden at Owens’s trial.
At the time of her death, Graves was a 41-year-old single mother of three.
Lawyers for Owens tried to halt his execution a few times, including twice in September. But the court denied each request.
In the latest attempt, lawyers pointed to an affidavit signed by Golden on Wednesday, which claimed Owens was innocent.
The court denied the request to halt the execution by saying that the new affidavit was “squarely inconsistent with Golden’s testimony at Owens’s 1999 trial” and the statement he gave to police right after their arrest.
Other witnesses testified that Owens had told them he shot Graves, prosecutors said.
Advocates against the death penalty and Owens’s mother also appealed to the state for clemency, which was denied by Governor Henry McMaster.
Hours before his execution, Owens’s mother said in a statement it was a “grave injustice that has been perpetrated against my son”.
“Freddie has maintained his innocence since day one,” his mother, Dora Mason, said, according to local news outlet the Greenville News.
Inmates in South Carolina are allowed to choose whether they want to die by lethal injection, electric chair or firing squad.
Owens deferred the decision to his lawyer, who chose the lethal injection option for him, according to the Greenville News.
Journalists who witnessed the execution said members of Graves’ family were also present.
(Except for the headline, this story has not been edited by PostX News and is published from a syndicated feed.)