Villa achieved his first international hat-trick on 10 June 2008 when he scored the first three goals in a 4–1 victory for Spain over Russia during UEFA Euro 2008 to win group D. He has scored two other hat-tricks, against Azerbaijan (in 2009) and Tahiti (in 2013).
Villa mencetak hat-trick internasional pertamanya pada 10 Juni 2008 saat ia mencetak tiga gol pertamanya dalam kemenangan 4–1 untuk Spanyol atas Rusia pada UEFA Euro 2008 untuk memenangkan grup D. Ia mencetak dua hat-trick lainnya, saat melawan Azerbaijan (pada 2009) dan Tahiti (pada 2013).