Ramiro Hernandez-Llanas, 44, was in the US illegally when he killed a former university professor who had hired him to help with renovations on his home.
The execution by lethal injection went ahead after Texas’ parole and pardons board refused to delay his case.
Ramiro Hernandez-Llanas is the sixth Texas prisoner executed this year.
He was the second person this week to be executed in Texas by lethal injection with a new supply of pentobarbital.
Earlier this week, a US appeals court rejected a bid by lawyers for Ramiro Hernandez-Llanas and another death row inmate, Tommy Lynn Sells, to learn who is supplying Texas with the drug.
They argue they need to know the source to ensure the executions will not be botched.
But Texas officials have refused to identify the source of the sedative, saying secrecy is needed to protect the provider from threats of violence.
Ramiro Hernandez-Llanas was pronounced dead at 18:28 local time at the Texas state death chamber in Huntsville.
In a final statement, Ramiro Hernandez-Llanas asked forgiveness from the victim’s family and said he was at peace, the Associated Press reports.
In 1997, Glen Lich, 49, hired Ramiro Hernandez-Llanas to work for him to help renovate his ranch near the city of Kerrville.
Unbeknownst to Glen Lich, Hernandez-Llanas had recently escaped from a Mexican prison where he was serving a 25-year sentence for a 1989 murder.
Several days later, Ramiro Hernandez-Llanas lured Glen Lich away from his house by telling him falsely there was a problem with a generator. He beat the man to death with a length of steel rebar, then entered the house and attacked Glen Lich’s wife.
Sentenced in 2000 for Glen Lich’s murder, Ramiro Hernandez-Llanas was among more than four dozen Mexican nationals awaiting execution in the US in 2004 when the International Court of Justice in The Hague, Netherlands, ruled they had not been properly informed of their consular rights when arrested.
Another one of those Mexican nationals, Edgar Tamayo, 46, was executed by Texas in January despite objections of both the Mexican and US governments.
Euclides del Moral, a Mexico foreign ministry official, said on Tuesday “the execution of a Mexican national is of great concern”.
But the issue did not play a large part in Ramiro Hernandez-Llanas’ appeals, which focused primarily on claims that his mental impairment made him ineligible for the death penalty.
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