On Megillah 15a, Rabbi Yehoshua ben Korchah says that Malachi was Ezra. The sages disagree saying Malachi was a different person. Rav Nachman says Malachi was probably Ezra as they both castigated the jews for taking gentile wives.
This only seems to prove that Ezra and Malachi lived at the same time and were both concerned about the major sin that the jews had committed. How does it prove they were the same person?
The gemora says that R’ Nachman says that the reason it makes sense that they are the same person because Malachi chastised them and Ezra separated the families that sinned from the rest of the Jews. My understanding of this is that R’ Nachman reasons that the same person who was tasked with making sure that they would not sin and defile Klal Yisroel, was the same person separated those who did sin, so that Klal Yisroel should not get defiled.