Police Chief Ray Schultz said Tiffany Toribio, 23, told officers that she and her son, Tyruss "Ty" Toribio, were in Alvarado Park before dawn on May 13 and that she suffocated him while he was asleep.
She told detectives she had second thoughts and performed CPR on the boy, reviving him, but again reconsidered and placed her hand over his nose and mouth until he suffocated, Schultz said. She said she waited a few minutes before burying him in the playground, the chief said.
Ty's body was found Friday by a mother who saw his black tennis shoe sticking out of the sand. Police released an artist's rendering of the boy's image on Tuesday, which led to tips about Toribio from family members and others, Schultz said.
Police picked up Toribio after she called them late Wednesday saying she had left home and was walking to the police station to turn herself in, the chief said. At first she denied being Tiffany Toribio, but officers found her identification and she acknowledged who she was, he said.
Neither the district attorney's office nor police knew if Toribio had an attorney, but she would have to have representation by her Friday arraignment.
Schultz called it "somber day" in Albuquerque.
"He was a very special child and that's what makes this case so hard for everybody within the Albuquerque Police Department that's worked on it for the last six days," he said.
At the playground - filled now with flowers, plaques and candles - about a dozen people gathered, some part of the regular vigil held there since last week and others who came down after hearing of the arrest on the TV news.
"We named him 'Baby Angel' and it's important now that we know his real name," said Sarah Sandoval, who lives nearby. "Now, his mother will find out this baby has a lot of people who love him and will do anything for a child."