Jeromie Cancel, 22, was arrested Tuesday on murder charges.
Investigators said that while Cancel was being questioned in an unrelated case, he admitted suffocating Pravia and stealing his cell phone, laptop computer and iPod.
Police said Cancel, who smiled for television cameras as he was being led in handcuffs out of a police station, was homeless, and they were unsure whether he had an attorney.
Cancel's father, Jesus Soto, said his son had stolen various possessions from him in June, and he called police when Cancel showed up at his apartment Monday night.
"You don't take someone's life like that," the father said. "He deserves what he gets."
Cancel claimed that Pravia approached him in Union Square park around 6 a.m. Saturday looking for drugs and that the two went to his apartment in the Chelsea neighborhood, police said. After the slaying, Cancel stayed in the apartment to watch the gory horror film "Saw" before leaving before 11 a.m., police said.
No drugs were found at the scene, police said.
The medical examiner's office said an autopsy was inconclusive and additional tests were being performed to determine what caused Pravia's death.
Cancel told investigators that Pravia fell asleep and he decided to rob him, so he punched the student in the face, stuffed a bag in his mouth and wrapped the television cord around his neck, then suffocated him, police said. He said he sold the laptop on the street after leaving the apartment, sold the cell phone in a store and couldn't remember what he did with the iPod, they said.
Deputy commissioner Paul Browne said police recovered the phone where it had been sold.
Pravia, a sophomore at Pace University, was from Peru, Mass., about 10 miles from the New York border.
Pace officials offered sympathy to Pravia's family. Grieving friends quickly cobbled a Facebook page dedicated to the student and expressing shock over his death.
Pravia was a 2007 graduate of Wahconah Regional High School in Dalton, Mass., where counselors were available Tuesday to help staff and students deal with the loss. Principal James Conro remembered Pravia as a "quiet, polite and respectful young man."
"My heart goes out to the family," Conro told The Berkshire Eagle, of Pittsfield, Mass.
