[1] He made his professional debut with the Dominican Summer League Rockies in 2012, making 18 appearances and registering a 3.71 ERA with 15 strikeouts and 2 saves in 17.0 innings pitched.

[2] Brazobán made 21 appearances for the Low-A Tri-City Dust Devils in 2013, struggling to a 7.78 ERA with 24 strikeouts in 19+2⁄3 innings of work.

[6] In 2017, he made 37 appearances split between the High-A Lancaster JetHawks and Double-A Hartford Yard Goats, posting a cumulative 5.77 ERA with 32 strikeouts and 5 saves in 39.0 innings of work.

[11] On March 4, 2021, Brazobán had his rights traded alongside Michael Martínez to the High Point Rockers of the Atlantic League of Professional Baseball.

[13] On January 4, 2022, Brazoban signed a contract with the Miami Marlins organization, where he was assigned to their Triple-A affiliate, Jacksonville Jumbo Shrimp.

On July 30, 2024, the Marlins traded Brazobán to the New York Mets in exchange for minor league infielder Wilfredo Lara.