On November 16, 2018, Tapia signed a minor league deal with the Boston Red Sox organization. In 2019, he played for the Pawtucket Red Sox, Boston's Triple-A affiliate, posting a 5–4 win–loss record in 44 games (1 start) with two saves, a 5.18 earned run average (ERA), and 52 strikeouts in 66 innings pitched. Through 2019, including with Pawtucket, Tapia appeared in 242 games in 10 seasons of Minor League Baseball, accruing a 38–50 record with 4.14 ERA and four saves. He also played four seasons in the Dominican Winter League, with Gigantes del Cibao.
