Hours after the arrest, authorities found two bodies matching the description of bagel shop owner Lisa Underwood and her son, Jayden, authorities said.
Stephen Dale Barbee, 37, admitted arguing with Underwood over leaving his wife, according to court papers. Barbee allegedly said he suffocated Underwood, and then did the same to the boy after he interrupted the attack.
Court papers said Barbee was the father of Underwood's fetus.
Barbee was arrested in Tyler, where he had been working clearing trees.
Underwood told investigators he put the bodies in the back of his sport utility vehicle and dug a shallow grave. The SUV was found in a creek near the town of Denton on Monday.
Court papers also revealed that a sheriff's deputy briefly had Barbee in custody early Saturday when he stopped a suspicious man covered in mud. The man ran into the woods and escaped.
Underwood, who was seven months pregnant, was reported missing Saturday along with her son after she failed to show up at her baby shower. A pool of blood was found in her Fort Worth home, but there was no sign of forced entry, police said.
Underwood and Barbee met about two years ago but split up last fall because Barbee had another girlfriend, said Debbie Lindley, a neighbor of Underwood's.
On Monday, Underwood's sport utility vehicle was found partially submerged in a creek near Denton.
CBS News Correspondent Drew Levinson reports police on horseback as well as inmates on foot searched the surrounding farmland for hours, but came up with nothing.
Acting on an anonymous tip, police searched a Fort Worth home during the night and found an item referred to by the tipster, but officials would not say what it was or how it figured in their investigation.
Jones said he didn't know why Barbee was in Tyler, how investigators knew to find him there or whether there were other suspects.
"We haven't established a motive, so I can't speak to that," Jones said.