The convict, Rodney Reed, was to die by lethal injection on November 20, Efe news reported.
With the Texas Criminal Court of Appeals' decision, the case now has returned to the trial court to consider new pieces of evidence presented.
The stay in his execution came after the Texas Board of Pardon and Paroles unanimously recommended Governor Greg Abbott to delay the death sentence by 120 days.
Reed, a 51-year-old African-American, was sentenced to death for the murder of Stacey Stites, a 19-year-old white girl whose body was found near Bastrop area close to Austin.
Reed's lawyers, represented by Project Innocence, have for the past few years filed new evidence, alleging that Stites's fiance Jimmy Fennell was responsible for the murder.
Reed and Fennel, a former police officer, have been accused of several sex crimes.
Although Reed was never sentenced for those cases, Fennell spent 10 years in prison for kidnapping and raping a woman in 2007 while on duty.
Reed became the main suspect in the case after traces of his semen were found on Stites' body.
Reed has maintained that he and Stites were having an affair - a version corroborated by former colleagues and a relative of the victim. He also alleged that Fennell had killed her for the same.
Reed's lawyers have requested the DNA results, based on which she was believed to have been murdered, to be looked into along with the ones found at the site of the murder such as the evidence found near Fennell's vehicle.
Texas has the highest number of death penalty sentences with 566 - eight executions in 2019 - of the 1,510 executions across the country since it was re-imposed in 1976.
( With inputs from IANS )