Inside the apartment, Morris and the other man, who has not been identified, fought over a knife until Morris was stabbed. At least one other person was in the apartment at the time, police said.
Police responded to a call of a break-in under way and found Morris dying from stab wounds when they arrived, officials said.
Drexel University said the stabbing grew out of an altercation involving "a student from another university."
Police questioned the man who allegedly stabbed Morris and spoke with several other witnesses.
Police said officers got the call about 4:55 a.m. to go to the 3400 block of Race Street in Powelton Village for a man who had kicked in the front of door of duplex housing apartments.
The street borders the Drexel campus.
On arrival, the officers found Morris on the second floor with stab wounds to the chest, cheek and head, police said.
Medics took him to the Hospital of the University of Pennsylvania, where he was pronounced dead at 5:58 a.m., police said.
A young man and young woman who left the gray stone duplex om the tree lined street this morning declined to say anything and drove off in a black Jeep.
Passerby Kevin Patterson, 21, a rising junior at Drexel from Bucks County said he was upset he had not learned about the stabbing via the university's crime alert system.
"We have a great crime reporting system," he said. "They tell you everything from the details of the crime to safety tips."
The university said a DrexelALERT was not sent because the person who allegedly stabbed Morris was in police custody and there was no threat to the public.
Drexel said its Counseling Center was offering assistance to "members of the community who have been affected by this tragic event."
Daily News staff writer Dana DiFilippo and Inquirer staff writer Allison Steele contributed to this article.
Contact the Online Breaking News Desk at email@example.com or 215-854-2443.