Bryan Lamont Weeks, 24, of 4529 Bumphas Road, was arrested by Orange County Sheriff's Deputy Steve Minton, who responded to a 911 call one of the victims made at 3:16 a.m.
A 911 operator told Minton that the victim who placed the call said the assailant was her son. The caller also said he had fled in a car.
The victims, Susie White Carrington, Weeks's mother, and Klim McCoy Carrington, both of 4529 Bumphas Road, are listed in critical condition at UNC Hospitals.
As he approached Bumphas Road, Minton observed a vehicle turning right off of Bumphas onto New Hope Road.
The car's driver did not stop for the deputy's blue lights, so Minton pursued the vehicle into the Durham city limits.
After the vehicle blew a tire at the intersection of Avondale and Trinity avenues, the driver stopped the vehicle and fled on foot.
A short chase ensued and Minton apprehended the suspect, later identified as Weeks. He was charged with various traffic violations, soon followed by other charges.
Deputies also found and seized a firearm visible on the floorboard of Weeks's car.
Based on statements made by Weeks, he was then charged with two counts of assault with a deadly weapon with intent to kill, inflicting serious injury.