Staff at the state prison in Huntsville said the execution by lethal injection was completed at 6:27 p.m.
Basso, 59, was put to death for her role in the 1998 torture-slaying of a mentally impaired man, Louis Musso, 59, in suburban Houston.
Basso was among six assailants who attacked Musso with belts, baseball bats, steel-toed boots and their hands at his home in Jacinto City. He also was doused with a solution of bleach and pine cleaner and scrubbed with a wire brush.
Basso had promised to marry Musso and was to have been the beneficiary of his insurance policy, authorities said. Basso convinced him to move from New Jersey to Texas.
The other defendants are in prison.
KWTX-TV, Waco, said the U.S. Supreme Court rejected Basso's appeal about an hour before her execution. Her attorney argued unsuccessfully she was mentally incompetent to be executed and the state law regarding competency was unconstitutional.
The Death Penalty Information Center said Basso was the 14th woman among at least 1,365 inmates executed in the United States since 1976. More than 3,100 inmates are sitting on death row in prisons across the country.