Banks' claims that he was wrongly convicted of a murder 23 years ago were backed by three former federal judges.
His lawyers told justices he was poorly represented at trial, prosecutors improperly kept blacks off the jury and testimony from two prosecution witnesses was shaky. Banks is black, his victim was white and the jury was all white.
The court issued the stay, without comment, about 10 minutes before the 44-year-old was to be put to death for the 1980 murder of 16-year-old Richard Wayne Whitehead, a co-worker at a restaurant. Banks allegedly said he shot Whitehead "for the hell of it" after a night of drinking, according to a witness who testified at the trial.
Banks has been on death row 22 years, longer than Whitehead was alive.
One of the three former federal judges supporting the Supreme Court intervention was former FBI Director William Sessions, who submitted a brief to the high court in which he cited "uncured constitutional errors" in Banks' case.
The Texas Court of Criminal Appeals this week refused to block Banks' execution, and the Texas Board of Pardons and Paroles would not hear his plea because it was filed too late.
The majority of last-minute death row appeals are rejected by the Supreme Court, although justices have stopped a handful of executions in the past few years. Last year, the justices blocked executions in Florida, Tennessee and Texas.
The Texas inmate who received a stay, Thomas Miller-El, won his Supreme Court appeal last month. The court ruled that Miller-El, who is black, deserved a new chance to press his claim that prosecutors stacked his jury with whites and death penalty supporters.
The stay in Banks' case will remain in effect until the court decides whether to review his case. No justices noted objections to the reprieve.
Prosecutors and the victim's family have insisted Banks received a fair trial.
"All these articles about poor Delma, poor Delma and how much of a raw deal he got," said Larry Whitehead, the victim's father. "Stopping a youngster's life at 16 years old is a raw deal."
Sessions and others had told the court in a filing that the claims raised in the appeal "go to the very heart of the effective functioning of the capital punishment system."
Texas accounts for more than one-third of the 835 executions in the United States since the U.S. Supreme Court in 1976 allowed capital punishment to resume. Virginia has the second-highest total, with 87.
On Tuesday, murderer Bobby Glen Cook became No. 299 since Texas resumed capital punishment in 1982. It was the 10th execution this year in Texas, which is on a pace to top the record 40 lethal injections carried out in 2000.