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Brandi Glanville caught a dude red-handed ... allegedly breaking into her Range Rover, and the whole incident was caught on camera -- including a foot chase to nab the suspect.

It all went down Sunday afternoon on Ventura Blvd. in the San Fernando Valley -- Brandi was walking up to her whip just as the alleged thief was going to work. He tried to flee the scene, but another guy -- possibly Brandi's friend -- gave chase on foot.

A photog who happened to be shooting the former 'Real Housewives' star captured the crazy scene, and even followed the action down the road ... as Brandi's friend pinned the suspect down until police arrived to arrest him.