Three and a half hours before he was scheduled to die by lethal injection, Richard Glossip won a two-week reprieve on Wednesday from an Oklahoma appeals court, which said it wanted time to study new evidence filed by his lawyers the day before.

Mr. Glossip, 52, was at the center of a major Supreme Court case in June on lethal injections. Along with two other condemned inmates, he had challenged Oklahoma’s use of a new drug combination as unconstitutional, saying it could cause extreme suffering. But the justices rejected the argument, 5 to 4, and his execution was set for 3 p.m. Wednesday.

His case received national attention, with Sister Helen Prejean, the anti-death-penalty activist, the Innocence Project and others saying that there were serious questions about Mr. Glossip’s guilt.

A new team of lawyers produced accounts from two people that, they said, demolished the credibility of the main witness who had implicated Mr. Glossip, who was not tied to the crime by any physical evidence.