The chase started at about 7:30 a.m. on Tuesday after a California Highway Patrol officer saw a blue Crown Victoria go through the car pool lane with two people inside instead of three.
The driver refused to stop and headed westbound, hitting two cars at the base of the bridge.
He then led officers across the bridge at speeds above 85 miles an hour, weaving across all lanes.
The car exited at Fifth Street and after hitting a parked car and eventually spun out at 16th Street and Mission.
"We were then able to take him into custody, and subsequently found a loaded handgun in the vehicle. The party was arrested along with his passenger for the violations observed. And an investigation is continuing now," said Dana Smith from the California Highway Patrol.
No one was hurt during the high-speed pursuit.