The court's action, announced Tuesday, came in the case of a man who came within minutes of execution before the body stepped in last year to stop it.
Delma Banks, one of the country's longest-serving death row inmates, was sentenced to die for the 1980 killing of a 16-year-old former co-worker at a fast food restaurant.
The high court's 7-2 ruling means Banks can continue to press his appeals in lower courts.
He claims that prosecutors lied and that his original defense lawyer did not do enough to help him.
"When police or prosecutors conceal significant exculpatory or impeaching material, we hold, it is ordinarily incumbent on the state to set the record straight," Justice Ruth Bader Ginsburg wrote for the high court majority.
Chief Justice William H. Rehnquist and Justices John Paul Stevens, Sandra Day O'Connor, Anthony M. Kennedy, David H. Souter and Stephen Breyer fully agreed with Ginsburg.
"A rule declaring 'prosecutor may hide, defendant must seek,' is not tenable in a system constitutionally bound to accord defendants due process," Ginsburg said.
Justices Clarence Thomas and Antonin Scalia did not agree that Banks got a raw deal from prosecutors, but still would have sent his case back to a federal appeals court for further consideration.
Texas prosecutors said Banks lured Richard Whitehead to a quiet park and shot him three times to steal his car. Banks maintains he is innocent, and that he was framed by lying witnesses who were bought off by the state.
Banks' backers including former FBI Director William Sessions, and a group of former judges say Banks' case is a textbook example of the wrong way to run a capital trial.
Prosecutors knew of numerous serious legal errors during Banks' trial, but said nothing, Banks' new lawyers contended.
Banks was scheduled to die last March, and was nine minutes away from execution when the Supreme Court stepped in and agreed to hear his case.
Banks claims his original lawyer failed to present evidence about Banks' family and background that might have persuaded a jury to spare Banks a death sentence.
The case also raised questions about how to weigh the severity of courtroom errors long after the fact.
Banks claims prosecutors improperly sat on evidence that could have undermined the testimony of a key witness for the state. The witness later recanted parts of his testimony. Banks also claimed that prosecutors hid the fact that another trial witness was a paid informant.
The facts of the Banks case are tangled and unusual, meaning that Tuesday's ruling in his favor may have little effect on other death row inmates or on future prosecutions.
Throughout 24 years of court fights, the parents of Richard Whitehead have insisted on Banks' guilt while Banks and his mother have insisted on his innocence.
The Whiteheads were waiting at a Texas prison the night Banks was to die.
The case is Banks v. Dretke, 02-8286.
The Supreme Court Tuesday also:
The court, in the 6-3 decision, said a federal anti-discrimination law is meant to protect older workers from preferential treatment given to younger workers, but the law does not apply in reverse.
"The dissenters on the Court argued that age discrimination is age discrimination no matter which age group is being discriminated against but that argument did not hold," says CBS News Legal Analyst Andrew Cohen. "The Court's majority ruled that younger employees could not rely upon this federal age discrimination law to sue their employers who were given better benefits to older employees."
The case is General Dynamics Land Systems Inc. v. Cline, 02-1080.