This phase III trial compares the effect of bevacizumab and AZD9291 (osimertinib) combination vs. osimertinib alone for the treatment of non-small cell lung cancer that has spread outside of the lungs (stage IIIB-IV) and has a change (mutation) in a gene called EGFR. The EGFR protein is involved in cell signaling pathways that control cell division and survival. Sometimes, mutations in the EGFR gene cause EGFR proteins to be made in higher than normal amounts on some types of cancer cells. This causes cancer cells to divide more rapidly. Osimertinib may stop the growth of tumor cells by blocking EGFR that is needed for cell growth in this type of cancer. Monoclonal antibodies, such as bevacizumab, may interfere with the ability of tumor cells to grow and spread. Giving osimertinib with bevacizumab may control cancer for longer and help patients live longer as compared to osimertinib alone.