Two men had just left a bar in southwest Houston and were on their way home when they were attacked, investigators said.
Houston police said say two people robbed the men on Beechnut near Commerce Park about 1 a.m.
Detectives said one of the attackers pulled a knife and started stabbing one of the victims. That man later died at a hospital. His name has not been released.
The second victim was not wounded and ran away, investigators said.
Police said a Harris County Precinct 5 deputy constable who was on patrol in the area witnessed the slaying and started chasing the two suspects.
The men ran into a nearby apartment, officials said. When police arrived, the men had escaped, presumably through a back window, detectives said.
Investigators spoke with neighbors and others who live in the area to try and track down leads.
Detailed descriptions of the attackers have not been released.
Anyone with information is asked to call Crime Stoppers at 713-222-TIPS.