The court's ruling leaves unanswered, however, broader questions about the chemicals used in lethal injections around the country and whether they cause excruciating pain.
"While these aren't rulings on the merits of these cases they are significant - and good news for death penalty opponents - because they are a clear sign from this newly-constituted Court that it still is concerned about procedure in capital cases," CBS News legal analyst Andrew Cohen says.
The ruling sets the stage for a nationwide legal battle over that subject, with the country's 3,300 death row inmates armed with a new tool to contest how they are put to death. Justices have never ruled on the constitutionality of a specific type of execution. A constitutional showdown over lethal injection might be the next big death penalty case.
The winner in Monday's decision was Florida death row inmate Clarence Hill, who was strapped to a gurney with lines running into his arms to deliver the drugs when the Supreme Court in January intervened and blocked the execution.
Justice Anthony M. Kennedy, writing for the court, said that while Hill and other inmates can file special appeals, they will not be always entitled to delays in their executions.
"Both the state and the victims of crime have an important interest in the timely enforcement of a sentence," he wrote.
Hill, convicted of killing a police officer, had run out of regular appeals so he went to court using a civil rights law claiming that his constitutional rights would be violated by Florida's lethal injection drug protocol. The court's decision renews his bid to have Florida change its chemical combination.
The decision is setback for Florida and other states that will have to defend more last-minute filings from inmates. More than two dozen states had filed arguments at the court seeking the opposite outcome. They said dragged-out appeals jeopardize justice for victims' families.
Lethal injection is the main method used by every state that has capital punishment except Nebraska. Nebraska still has the electric chair, although that, too, is being contested.
Kennedy said that Hill is not claiming that he cannot be executed, only that he should not be forced into a painful execution.
"Hill's challenge appears to leave the state free to use an alternative lethal injection procedure," Kennedy wrote.
In other ruling about death row-inmates, the Supreme Court also ruled Monday that a Tennessee death-row inmate can use DNA evidence to attempt to show his innocence 20 years after he was convicted of murdering a neighbor.
The high court's decision in this case is significant because numerous exonerations in recent years of death-row and other criminal defendants through DNA testing have raised concerns among civil libertarians, prosecutors and Supreme Court Justice John Paul Stevens that an innocent person may be executed, or already has been.
"This ruling is a direct result of the Court's growing acceptance of DNA evidence as a tool, especially in capital cases," Cohen said. "But it is a very narrow ruling and won't automatically mean we'll be seeing death row inmates everywhere getting to make this sort of an argument at this stage of their case."
Justice Anthony M. Kennedy, writing for the court, said the evidence in the case was a "close" call for a jury. But he said that inmate Paul Gregory House could proceed with a lawsuit in federal court claiming innocence for the murder of Carolyn Muncey, a young mother of two, in Union County, Tenn., in July 1985.
Twenty years after his conviction, DNA testing revealed that semen found on the murder victim's nightgown and underwear belonged to her husband, not House.