On a winter day in 1981, the body of a newborn baby was found abandoned in a ditch near a cornfield in Sioux Falls, S.D. He had been wrapped in a blanket. Tears were frozen on his cheeks.

After no one reported him missing, residents in Sioux Falls named him Andrew John Doe. He was eventually laid to rest in a local cemetery, where he remained unidentified, but not forgotten, for nearly four decades, a court document said.

Now the authorities believe they have solved the case. On Friday, the Sioux Falls Police Department said that investigators had finally tracked down the baby’s mother, a 57-year-old woman in Sioux Falls named Theresa R. Bentaas, using DNA testing and genealogy databases. She was arrested that day and faces murder charges, the department announced at a news conference.

Chief Matt Burns said the arrest was the outcome of years of persistence. Even as tips went nowhere and lines of investigation went thin, he said, detectives pressed on “in the hope of generating a lead, stirring a memory or burdening a conscience to confess.”

The turning point in the case, which highlights how DNA technology is increasingly being used to solve old homicides, came in 2009, Chief Burns said. That was when Michael Webb, a detective at the department, took the lead in pursuing the investigation using technology and databases that were not available to his predecessors.

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The case was “cold,” Detective Webb said at the news conference, but it was never “closed.”

“We don’t forget about these cases — we never do,” he said. “You work pretty hard when it is a child case.”

Ms. Bentaas is being held on murder and manslaughter charges, but the final charges will be determined by a grand jury or in a preliminary hearing on March 26, Crystal Johnson, a prosecutor working on the case, said in an interview on Tuesday. Ms. Bentaas is being held in Minnehaha County Jail with bail set at $250,000, according to records from the county sheriff’s office.

She had an initial appearance in front of a judge on Monday, Ms. Johnson said.

Raleigh Hansman, a lawyer for Ms. Bentaas, declined to comment on Tuesday, and calls to Ms. Bentaas’s family members were not answered.

Advances in DNA technology and genealogy databases have recently helped the authorities find suspects in a number of old murder cases, including the search for the Golden State Killer in California. Some of these cases, like the Sioux Falls one, have involved the identification of mysterious remains, Detective Webb said.

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“These cases are frustrating and disappointing,” he said. “You are going to learn you have more failures than successes. We persisted on.”

The story of the Doe baby started on Feb. 28, 1981, when Lee Litz, a Sioux Falls man, was test-driving a car and spotted a pile of “wine-colored” blankets near the road, he said in a recent interview with The Argus Leader, a Sioux Falls newspaper. He stopped to examine the blankets out of curiosity because they looked new, he said.

Wrapped up in the bundle was the dead baby. The placenta was still attached. Clothing with traces of blood was found nearby, the arrest affidavit for Ms. Bentaas said.

“I just wish I could have found him earlier when he was still alive,” Mr. Litz said.

An autopsy said the baby had been born alive, most likely on Feb. 27, and had probably died of exposure, according to the affidavit.

Detectives could not locate the mother or family members of the infant, and the case went cold. The baby was buried in St. Michael Catholic Cemetery, with about 50 residents paying respects at the graveside, the affidavit said.

When Detective Webb picked up the case in 2009, he obtained a court order to exhume the body for DNA testing, and the remains were transported to the University of North Texas Health Science Center, where a DNA profile was obtained, the affidavit said.

The baby’s remains were reburied on June 16, 2010, it said.

The DNA was sent to Parabon NanoLabs, which worked with law enforcement agencies to help identify possible suspects and relatives. The findings helped investigators unspool members of a family tree, helped by GEDMatch.com, Ancestry.com and findagrave.com, according to Detective Webb and the affidavit.

The findings eventually led the authorities to a residence in Sioux Falls where Ms. Bentaas was living, the affidavit said. They went through the trash. A package wrapper in the trash was addressed to her. A water bottle, cigarette butts and a beer can had female DNA on them that “could not be excluded” from a profile of the baby’s biological mother, according to the affidavit.

The father of the baby was not aware of the pregnancy and has not been charged, the affidavit said.

Ms. Bentaas spoke to investigators on Feb. 27 of this year, the anniversary of the day the baby is believed to have been born.

She said that in 1981 she was “young and stupid,” the affidavit said. She said she hid her pregnancy from family and friends, gave birth alone in her apartment, and then drove the baby, who was in the passenger seat, to the place by the road where he was later found, it said.

She was “sad” and “scared” as she drove away, the affidavit quoted her as saying. Asked if she thought about it when she drove by the spot now, she said, “Of course.”