Four liberal justices said they would have halted the execution, but five were needed to do so.
Smith was convicted of capital murder in the November 8, 1994, shooting death of Huntsville store clerk Casey Wilson.
A jury voted 7-5 to recommend a sentence of life imprisonment, but a judge overrode that recommendation and sentenced Smith to death.
Wilson was pistol-whipped and then shot in the head during the robbery, court documents show.
Surveillance video showed Smith entering the store and recovering spent shell casings from the bathroom where Wilson was shot, according to the record. Smith's lawyers had urged the nation's highest court to block the planned execution to review the judge's override.
Lawyers for the state argued in a court filing Tuesday that the sentence was legally sound, and that it is appropriate for judges to make the sentencing decision.
Judge Lynwood Smith, now a federal judge, sentenced Smith to death. He likened the killing to an execution, saying the store clerk was beaten into submission before being shot in the head in a crime that left an infant fatherless.
In overriding the jury's recommendation, the judge also noted in court records that, unlike many other criminal court defendants, Ronald Smith came from a middle-class background that afforded him opportunities.
In a clemency petition to Governor Robert Bentley, Smith's lawyers said he was an Eagle Scout at 15 and was the son of a NASA contract employee whose life spiralled downward because of alcoholism and emotional scars from an abusive home environment.
Smith had a final meal of fried chicken and french fries and was visited during the day by his parents and son.
None of Smith's family members attended the execution.
"For more than two decades Ronald Bert Smith has avoided justice for the cold blooded murder of Casey Wilson, who was first pistol whipped and shot in the arm after refusing to open a convenience store cash register and then shot in the head and left to die. The trial court described Smith's acts as 'an execution style slaying.' Tonight, justice was finally served," Alabama Attorney General Luther Strange said in a statement issued after the execution.
Alabama has been attempting to resume executions after a lull caused by a shortage of execution drugs and litigation over the drugs used. The state executed Christopher Eugene Brooks in January for the 1993 rape and beating death of a woman.
The following States in the US have the death penalty: Alabama, Arizona, Arkansas, California, Colorado, Florida, Georgia, Idaho. Indiana, Kansas, Kentucky, Louisiana, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, North Carolina, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, Washington and Wyoming.