A valve bridge is disclosed for use with an internal combustion engine. The valve bridge may include a body with a central cavity formed in a center portion of the body for receiving a hydraulic lash adjuster, and opposing first and second lateral extensions on opposite sides of the central cavity. The valve bridge may further include a first bore in the first extension for receiving a first valve stem, and a second bore in the second extension for receiving a second valve stem. The valve bridge may also include a first internal groove in a wall of the central cavity configured to receive fluid, as well as a first internal passage in the body that extends from the first internal groove toward the first bore. In addition, the first internal passage may extend from a higher gravitational point within the body to a lower gravitational point within the body.