The Supreme Court on Tuesday gave the only woman on death row in Oklahoma a fresh opportunity to challenge her sentence and conviction, saying that prosecutors may have violated her right to a fair trial by introducing lurid evidence about her sexual activities.

The woman, Brenda Andrew, was convicted of murdering her husband. Her trial was tainted, the majority said in an unsigned opinion, by “evidence about Andrew’s sex life and about her failings as a mother and wife.”

“Among other things,” the opinion added, “the prosecution elicited testimony about Andrew’s sexual partners reaching back two decades; about the outfits she wore to dinner or during grocery runs; about the underwear she packed for vacation; and about how often she had sex in her car.”

During closing arguments in 2004, a prosecutor dangled Ms. Andrew’s thong underwear before the jury. She had packed the undergarment for a trip to Mexico a few days after her estranged husband was killed.

The prosecutor said the item was strong evidence that Ms. Andrew had murdered her husband. “The grieving widow packs this to run off with her boyfriend,” he said, holding her underwear.

“That’s enough,” he said. “Can’t twist the facts, folks. Can’t twist the evidence.”

The spectacle “drew gasps from the crowded courtroom,” a local newspaper reported.