Police detained an 18-year-old man for questioning after officers located the car involved in the shooting at about 9 p.m. at a home on North Buena Vista Avenue.
No one was injured in the shooting, police said.
The incident started after a woman pulling out of a Piedra Vista High School parking space nearly hit another car, said Georgette Allen, a Farmington Police Department spokeswoman.
The driver of that vehicle, a red, four-door passenger car, followed the woman as she drove from College and Piñon Hills boulevards and turned south on Butler Avenue.
The woman told police that at about 8:20 p.m. she was at Butler Avenue and 30th Street and saw something long sticking out of the other vehicle and then heard a gunshot, Allen said.
The woman told police the driver of the car was a man wearing glasses and a beanie cap, said Farmington police Cpl. Travis Spruell.