This is an open-label phase II clinical trial designed to allow a preliminary assessment of the efficacy and safety of cabozantinib in unselected Non-Small Cell Lung Cancer (NSCLC) patients with metastases to the brain and in the subset of patients with c-MET amplified Non-Small Cell Lung Cancer with metastases to the brain. Previously treated patients with non-squamous NSCLC who have had brain metastases at any point in their treatment history are eligible for enrollment on this clinical trial. Patients with clinically asymptomatic untreated brain metastases will be allowed on trial at the discretion of the treating investigator. Patients who have undergone treatment for their brain metastases with Whole-Brain Radiation Therapy (WBRT), stereotactic radiosurgery (SRS) or surgery must be clinically stable and recovered from all procedures at the time of study enrollment.