Walter Storey, 47, died by lethal injection ten minutes after midnight (0610 GMT) in the town of Bonne Terre, said Mike O'Connell, spokesman for the state prison system.
Storey had been convicted 25 years ago of killing a neighbor, a 36-year-old social worker, by stabbing and beating her to death, after learning his wife wanted to divorce him.
His final appeal was rejected by the nine-member Supreme Court six hours before the execution.
Storey's argument was the same as those of three death row inmates in Oklahoma whose planned execution the court has in fact delayed and agreed to study.
Storey's attorney, Jennifer Herndon, had argued that the lethal injection technique used was illegal on grounds of the unreasonable suffering it can cause to inmates.
She said the reasons that the court had agreed to study in the Oklahoma cases justified a stay for Storey, AFP reported.
In April the court is scheduled to take up the issue of execution by lethal injection.
It could ban the use of midazolam, a barbiturate used in executions and associated with suffering by inmates, if it rules that it causes "cruel and unusual punishment" banned by the US constitution.
Midazolam is used as a sedative before executions in Missouri.
Executions are sometimes carried out in the US using it as part of a lethal cocktail that also includes the drug pentobarbital.
An execution in Oklahoma last year using midazolam in the case of man named Clayton Lockett was botched and the inmate was seen writhing in pain until he died.
"Missouri carried out 12 executions using pentobarbital since November 2013 and no observer has seen anything inconsistent with these executions all being rapid and painless," said Missouri Attorney General Chris Koster.
He said Missouri's method using midazolam as a sedative makes it impossible to compare with Oklahoma.
This was the eighth execution of the year in the United States and the first in Missouri, according to the Death Penalty Information Center.