Willie Shannon, 33, was convicted of the slaying of Benjamin Garza who was waiting for his wife and children in his car when he was attacked.
The Texas Department of Criminal Justice said Shannon, who was then 19 years old, entered the passenger side of the car and shot Garza in the head after a brief struggle.
He was later apprehended after being spotted driving the stolen vehicle. Police said he had raped a maid at a nearby hotel just 10 minutes before the slaying and carjacking.
In his last statement while strapped to the gurney, Shannon said he had not meant to kill Garza.
"I took a father, it wasn't my fault, it was an accident ... God knows the truth," he said.
Shannon had no last meal request.
Shannon was the 24th person executed in Texas this year and the 379th put to death in the state since it resumed capital punishment in 1982.
Texas, which has executed more people both this year and in the 20 years since the U.S. Supreme Court lifted a national death penalty ban, has one more execution scheduled this year.
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