[3] In 2009, he was promoted to the Danville Braves of the Appalachian League, where he made 14 appearances, including three starts and had a 3.05 ERA with two saves.

[1] In addition, he made appearances in all four games of the 2013 NLDS against the Los Angeles Dodgers, allowing three hits and no runs in 2+2⁄3 innings.

During his time with the Braves, Radio Announcer Don Sutton would often sing Avilan's name in a sing-song manner to the tune of Feliz Navidad.

[1] On July 30, 2015, in a three-team trade, the Los Angeles Dodgers acquired Avilán, Mat Latos, Michael Morse, Bronson Arroyo, Alex Wood, Jim Johnson, and José Peraza, while the Miami Marlins acquired minor league pitchers Victor Araujo, Jeff Brigham, and Kevin Guzman, and the Braves received Héctor Olivera, Paco Rodriguez, minor league pitcher Zachary Bird and a competitive balance draft pick for the 2016 MLB Draft.

[16] On January 4, 2018, Avilán was traded to the Chicago White Sox in a three-team trade that also sent Jake Peter and Scott Alexander to the Dodgers, Joakim Soria to the White Sox, and Trevor Oaks and Erick Mejia to the Kansas City Royals.

[17] On August 22, 2018, Avilán was traded to the Philadelphia Phillies in exchange for minor league pitcher Felix Paulino.

On January 10, 2019, Avilán signed a minor league deal with the New York Mets that included an invitation to spring training.

On August 28, Avilán was released by the Yankees two days after being placed on the injured list due to shoulder inflammation.

[24] On April 17, it was announced that Avilán had suffered a tear in his left UCL, requiring Tommy John surgery and ending his season early.

Avilán became a free agent following the season and re-signed with the Nationals on a minor league contract on November 29, 2021.

Playing in 36 games split between the High–A Wilmington Blue Rocks and Triple–A Rochester Red Wings, he recorded a cumulative 4.84 ERA with 39 strikeouts in 35+1⁄3 innings pitched.