Robert Roberson was found guilty in 2002 of the murder of his two-year-old daughter, but his scheduled execution was halted by the Texas Supreme Court.
He would have been the first person executed in the United States for a murder conviction connected to a shaken infant syndrome diagnosis.
Derrick Dearman, 36, was declared dead at 6:14 p.m. local time in Alabama after he urged a judge to execute his death sentence and dropped his appeal earlier this year.
Five people were slain in 2016 after Dearman, on a drug-fueled rampage, burst into a house where his ex-girlfriend had sought safety.
The Death Penalty Information Center reports that at least 20 people have been executed in the United States this year.
However, in recent decades, the numbers have been declining.
After weeks of public pressure and a flurry of last-ditch legal challenges, Roberson was granted a late-night stay of execution.
According to his supporters, faulty research led to his placement on death row.
Roberson waited for word on his fate in a jail cell in the Walls Unit in Huntsville, which is only a few meters from his nation’s busiest death chamber, in the hours before the decision.