Convicted killer James Jackson expressed love for his family before he was executed over the 1997 strangling of his two stepdaughters.
Prosecutors say Jackson also killed his 39-year-old wife, Sharon, during the attack at their Houston-area home.
The younger victims were 19-year-old "Sonnie" Mayes and her 18-year-old sister, Ericka.
Police say in his confession, Jackson said he and his wife had been arguing for several days over his unemployment and that she intended to divorce him.
Jackson was the fourth condemned killer to have his punishment carried out this year in Texas.
In his final statement, Jackson at one point turned to the warden and said, quote: "Warden, murder me."
The inmate then referred to Harris County, where he was convicted, as Sodom and Gomorrah, the biblical cities destroyed by God for their sins.
"I'm ready to roll. Time to get this party started," said Jackson, who seven minutes later was dead from the lethal drugs.