John Henry's death was the third execution since a botched injection in Oklahoma in April renewed a national debate over capital punishment.
Henry, 63, who previously served seven years for the manslaughter of his common-law wife, asked for forgiveness of his victims' families and Jesus in a brief final statement.
Henry's lawyers sought to have him declared mentally unfit for execution but the US Supreme Court rejected his last round of appeals.
Two convicted killers, one in Georgia and the other in Missouri, were put to death less than a day earlier.
The executions were the first since killer and rapist Clayton Lockett died in a mishandled execution in Oklahoma.