They found 34-year-old Michael James Copeland stabbed to death inside the home.
Officers say they spotted a man matching the description of the suspect about 30 minutes later near the intersection of Freeman and Clayton roads.
Police arrested 31-year-old Mico Langley and charged him with first-degree murder. He has been placed in Durham County Jail without bond.
Investigators say they are still looking into the circumstances surrounding the stabbing.
