Raphael Holiday became the 13th convicted killer put to death this year in Texas. The state has accounted for half of all executions in the US so far this year.
The lethal injection was carried out yesterday after the US Supreme Court rejected an appeal and after a state judge earlier in the day halted the punishment.
The Texas Attorney General's office appealed the reprieve, and the warrant was reinstated.
Holiday insisted he didn't know how the cabin north of Houston caught fire in September 2000, killing the children. His estranged common-law wife had obtained a protective order against him.