Scott Allen Hain had won the stay a day earlier from an appeals court. He was expected to be put to death Thursday night for helping to burn a man and woman alive in the trunk of their car in 1987.
Oklahoma had asked the court to intervene, arguing that Hain's appeals had run out.
The court's intervention seemed to shut the door on hopes by death row opponents that the court would soon consider banning executions of people who were juveniles when they committed their crimes.
The issue has been contentious for the court, which has held that states can put to death people who were 16 or 17 when they killed.
Last October, the four most liberal justices said the court should raise the age to 18.
"The practice of executing such offenders is a relic of the past and is inconsistent with evolving standards of decency in a civilized society," Justice John Paul Stevens said, along with Justices David H. Souter, Ruth Bader Ginsburg and Stephen Breyer.
The United States is one of a few countries that allow such executions.
The decision to allow the execution came from the court's conservatives: Chief Justice William H. Rehnquist and Justices Sandra Day O'Connor, Antonin Scalia, Anthony Kennedy and Clarence Thomas. The other four noted their objections.
Hain had won a reprieve from a panel of the 10th U.S. Circuit Court of Appeals in Denver, which voted 2-1 Wednesday night to stay the execution.
Hain is on death row for the killings of Michael Houghton, 27, and Laura Lee Sanders, 22, restaurant co-workers and friends, who were kidnapped Oct. 6, 1987, from behind a Tulsa bar and stuffed into the trunk of Sanders' car.
Hain was convicted with a man of taking the couple to a rural area and setting the car on fire.
Hain, now 32, says he acted under the control of Robert Lambert, a 21-year-old he had met on Tulsa's streets.
At issue in his appeal was whether the government should have paid for Hain's lawyer at a clemency hearing. An attorney appeared at the hearing with Hain, but said he could not present a credible case for clemency because he hadn't been able to prepare it, including bringing in experts to testify, because of lack of funds.
"If Hain would ultimately prevail in this appeal, it remains possible that he could persuade the Oklahoma Pardon and Parole Board to reconsider its decision and/or grant him a new clemency hearing," two 10th Circuit judges wrote.
Hain's lawyer, Steven Presson, said Hain talks about his regrets, describing haunting nightmares and dreams of trying to open the trunk but burning his hands.
Sanders' mother, Carol, was unmoved by Hain's apologies when he asked the parole board to spare his life.
"I don't know that he has heart to care," she said. "I think we're all looking forward to getting him out of our lives."
The murders ended what authorities said was a four-month crime spree by Hain and Lambert. The two were accused of sexually assaulting two Kansas women and later attacking a Tulsa couple, permanently injuring the man with a blow from a claw hammer and sexually assaulting and beating the woman.
Hain denied involvement in those attacks and was not tried for them after his conviction in the murders.