Officers said they got a call about an assault just after 3 p.m. in the 800 block of South Alston Avenue.
When they arrived, they found a woman hurt, and were told a man had been shot inside the Evans Mini Mart at 710 South Alston Avenue.
That man, 25-year-old Daniel Evans was pronounced dead at the scene.
Detectives said the woman was hurt in a fight with Evans and then several men chased him into the store where he was shot. The woman was taken to Duke University Hospital with non life-threatening injuries.
Police also want to talk to another man seen in the store. They sent out a surveillance camera picture to the media.
Anyone with information is asked to call Investigator Robinson at (919) 560-4440, ext. 29335 or CrimeStoppers at (919) 683-1200. CrimeStoppers pays cash rewards for information leading to arrests in felony cases and callers never have to identify themselves.