Last-ditch efforts are not uncommon in a death penalty case. But few legal sagas can match the twists and turns of the last few weeks in the case of Marcellus Williams, who faces execution on Tuesday night in Missouri.

On Monday morning, a prosecutor from the office that obtained the original death sentence 21 years ago will argue before the state Supreme Court that Mr. Williams’s conviction was flawed by violations of his rights during trial.

The hearing is one front in the accelerated effort by the defense team to spare the life of Mr. Williams, 55, who was convicted in 2003. His lawyers have filed an appeal to the United States Supreme Court, and the N.A.A.C.P., the Council on American-Islamic Relations and U.S. Representative Cori Bush of St. Louis have made pleas for mercy, saying that Mr. Williams was wrongfully convicted and that no physical evidence ties him to the crime.

“You have it in your power to save a life today by granting clemency to a man who has already unjustly served 24 years in prison for a crime he did not commit,” Ms. Bush, a Democrat, wrote to Gov. Mike Parson, a Republican. “I am urging you to use it.”

Since Mr. Williams’s conviction for killing Felicia Gayle, a well-known newspaper reporter, in her suburban St. Louis home in 1998, he has repeatedly come close to being spared, most recently last month.

His effort to prove his innocence has faced hurdles, including the deaths of two key witnesses against him; the abrupt exit from office of a previous governor, Eric Greitens, who had appointed a board of inquiry on the case; and evidentiary issues with the murder weapon that dashed Mr. Williams’s hope that DNA found on the weapon would point to a different suspect.

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