He played in Major League Baseball (MLB) from 2015 to 2019 for the Washington Nationals and the Pittsburgh Pirates.

He was an All-Star in 2018 and 2019 before his arrest on sexual assault charges led to his being placed on the restricted list by both the Pirates and Major League Baseball.

[3] On February 13, 2014, Vázquez was traded to the Washington Nationals, along with José Lobatón and Drew Vettleson, in exchange for Nate Karns.

[6] After the 2014 regular season, the Nationals assigned Vázquez to the Mesa Solar Sox of the Arizona Fall League.

[8] On April 17, 2015, Vázquez made his major league debut by coming in to pitch the top of the ninth inning in a 7–2 win over the Philadelphia Phillies.

With Jonathan Papelbon suspended and Drew Storen injured, Vázquez converted two save opportunities during the final week of the season.

[12] On July 30, 2016, the Nationals traded Vázquez, along with Taylor Hearn, to the Pittsburgh Pirates for Mark Melancon.

[14][15] After a 0.58 ERA in 31 games, on June 9 he was named co-closer for the Pirates along with Juan Nicasio, replacing Tony Watson.

In an April 7, 2019, game against the Cincinnati Reds, Vázquez was ejected after his role in a bench-clearing incident involving Chris Archer, Derek Dietrich, Yasiel Puig, Amir Garrett, Keone Kela, and David Bell.

[26] On September 17, the Pirates placed Vázquez on the restricted list, due to his arrest on multiple charges of unlawful contact with a minor.

[14] He also throws an effective changeup at 89–90 miles per hour (143–145 km/h) with two-seam movement, which he picked up in the Rays minor league system.

[15][30] In 2018, he changed his last name from Rivero to Vázquez to match the surname of his sister, citing that she had been a big part of his career.

[40] Another motion to dismiss the charges was filed in late 2020, this time over jurisdictional issues relating to the state in which the crimes allegedly occurred.