Davis has spent 18 years on death row for the 1989 slaying of Savannah police officer Mark MacPhail. Davis' attorneys insist that he is innocent and deserves a new trial because several witnesses at his trial have recanted their testimony.
The high court ordered a federal judge in Georgia to determine whether there is evidence "that could not have been obtained at the time of trial (that) clearly establishes petitioner's innocence."
Defense lawyers had appealed to the Supreme Court after a federal court denied a new trial request in April.
"The substantial risk of putting an innocent man to death clearly provides an adequate justification for holding an evidentiary hearing," said Justice John Paul Stevens, writing for the court. Justices Ruth Bader Ginsburg and Stephen Breyer concurred with Stevens.
MacPhail was slain while working off-duty as a security guard at a bus station. He had rushed to help a homeless man who had been pistol-whipped at a nearby parking lot, and was shot twice when he approached Davis and two other men. Witnesses identified Davis as the shooter at his 1991 trial.
But Davis' lawyers say new evidence proves their client was a victim of mistaken identity. They say three people who did not testify at Davis' trial have said another man confessed to the killing.
Davis' attorneys have delayed his execution three times by raising doubts about those witnesses. But state and federal courts have denied Davis' request for a new trial, and Georgia officials have repeatedly rejected calls for clemency.
The case has attracted worldwide attention, with calls to stop Davis' execution from former President Jimmy Carter, Pope Benedict XVI and Nobel Peace Prize-winner Desmond Tutu.
Justices Antonin Scalia and Clarence Thomas dissented from the decision to order an evidentiary hearing, with Scalia saying that "every judicial and executive body that has examined petitioner's claim has been unpersuaded."
Davis' "claim is a sure loser," Scalia said. "Transferring his petition to the District Court is a confusing exercise that can serve no purpose except to delay the state's execution of its lawful criminal judgment."
Scalia said the Supreme Court was sending the District Court for the Southern District of Georgia "on a fool's errand."
"That court is directed to consider evidence of actual innocence which has been reviewed and rejected at least three times," he said.
Justice Sonia Sotomayor, who was just confirmed as a new justice earlier this month, did not take part in the consideration of Davis' motion, the court said.
Davis' family said the ruling gives them hope that he could be exonerated.
"I'm always optimistic," said his sister Martina Correia, who has traveled around the world advocating for his case. "This means he gets another chance. And we're going to keep fighting for that chance."
State officials welcomed the ruling.
"Hopefully, this hearing will resolve the doubts about the verdict handed down by the Chatham County jury 18 years ago," Georgia Attorney General Thurbert Baker said in a statement.
MacPhail's family was not quite so conciliatory. Anneliese MacPhail, the officer's mother, said she was "in shock" and worries the ruling will plunge a family seeking closure deeper into turmoil.
The ruling comes as MacPhail's friends and former colleagues prepare for a rally at a Savannah courthouse to honor the 20th anniversary of his death.
"They are pussyfooting around it," she said. "This has gone on long enough. The courts have been through this two or three times and nothing has changed."
Associated Press Writer Greg Bluestein in Atlanta contributed to this report.