The jury convicted David Edenfield, 61, in the March 2007 sexual assault and choking death of young Christopher Michael Barrios.
The jury now must decide whether to sentence Edenfield to death or life in prison.
Edenfield is the first of three people to stand trial for the boy's slaying. His wife and grown son have also been charged with molesting and killing the boy, then hiding his body.
The sentencing phase of the trial began soon after the verdict, with Christopher's family telling jurors of the boy's smile brightened by stainless-steel caps on his front teeth and the grief that still lingers 2 1/2 years later.
"Sometimes you just want to die, or catch yourself looking for Christopher to come home as if it never happened," said Sue Rodriguez, Christopher's grandmother.
The boy lived in a Brunswick mobile home park where his father and grandmother had homes. He would pass the Edenfields' trailer when walking between them.
Because of pretrial publicity, the jury was selected from residents who live some 90 miles away, and the jurors were sequestered in Brunswick, 60 miles south of Savannah.
District Attorney Stephen Kelley, in his closing argument to the jury, described the slain kindergartner as a "precious blessing, thrown away in a trash bag."
"Why would anyone want to rape a child? Why would anyone murder a child?" Kelley said, sounding both close to tears and rage. "It tears the very fabric of my soul to shreds just thinking about those questions."
Kelley replayed for the jury portions of Edenfield's videotaped confession in which he described watching, along with his wife, as their grown son stripped the boy and molested him in their mobile home.
Defense Attorney James Yancey Jr. urged jurors not to assume Edenfield's confession was genuine. Edenfield, Yancey said, likely told police what they wanted to hear after investigators repeatedly assured him he'd done nothing wrong and wouldn't go to jail as long as he told the truth.
He described the defendant, who sat passively in the courtroom, as a man who worked long hours at a fast-food restaurant to support a wife and son, who left him feeling defeated.
He said Edenfield knew that his wife, Peggy Edenfield, was unfaithful to him and that their 34-year-old son, George Edenfield, was both mentally disabled and a convicted child molester whose behavior was beyond his father's control.
After the verdict, a forensic psychologist hired by Edenfield's attorneys told jurors that tests showed Edenfield to be "psychotic but technically competant to stand trial."
Dr. James E. Stark, whose testimony jurors would weigh during sentencing, said Edenfield showed symptoms of paranoid schizophrenia and had a lower-than-average IQ.
"He's in poor touch with reality," Stark testified. "He may have hallucinations and some kinds of delusional thinking."
In an earlier police interview from March 2007, also shown to the jury, Edenfield acknowledged he had been charged with incest in 1994, when he was accused of having sex with an adult relative who was not his son.
Edenfield pleaded guilty to the charge, but in the police interview he denied wrongdoing. He said the relative was angry with him and made up the accusation.