The shooting happened about 2 a.m. in the parking garage at 275 S. Indian Canyon Drive.
Marine Cpl. Allan DeVillena II, 22, was fatally shot after he repeatedly ignored orders to turn off his vehicle by two officers on bike patrol.
One of the officers climbed partially into the passenger window to stop the car but the Marine accelerated, striking the other officer, according to the Palm Springs Police Department. The Marine kept driving with the officer hanging out of the window until the car crashed near the garage exit.
The department said at some point, fearing for their safety and the safety of others, the officers opened fire.
Both officers were treated for injuries at a hospital and released. They have been placed on administrative leave while the department investigates.
DeVillena was pronounced dead at the scene.
A passenger, another Marine, was not injured. He was arrested for investigation of public intoxication and for an unrelated misdemeanor warrant, cited and released.
DeVillena, a San Jose native, was part of the 1st Marine Logistics Group based in Camp Pendleton. He served in Afghanistan and was stationed at Twentynine Palms.
The Associated Press contributed to this report.