Quintana pitched in Minor League Baseball for the Mets and New York Yankees organizations before becoming a free agent and signing with the White Sox before the 2012 season.

[2] In 2011, Quintana posted a 10–2 win–loss record and a 2.91 earned run average (ERA), with 88 strikeouts in 102 innings pitched for the Tampa Yankees of the Class A-Advanced Florida State League (FSL).

[4] Chicago White Sox' scouts Daraka Shaheed and Joe Siers, who watched Quintana pitch in the FSL the previous season, recommended that the team sign him.

After he started the season with a 1–2 win–loss record, a 3.06 ERA, and 26 strikeouts in 35 innings pitched for Birmingham, the White Sox promoted Quintana to the majors on May 7, 2012, in accordance with the new MLB rule allowing teams to carry a 26th man on their 25-man roster during the day of a doubleheader.

He made his MLB debut in the first game of the doubleheader, pitching 5+2⁄3 innings in relief, allowing no runs, one hit, and two walks while striking out three.

[6] Quintana was optioned back to Birmingham the next day, staying until May 24, when he was promoted to the Charlotte Knights of the Class AAA International League.

During a game against the Tampa Bay Rays on May 30, 2012, Quintana was ejected by umpire Mark Wegner after throwing a pitch behind Ben Zobrist.

He qualified as a "Super 2" arbitration eligible player after the 2014 season, activating a clause in his contract which made the deal worth a guaranteed $26.5 million.

[20] On July 13, 2017, the White Sox traded Quintana to the Chicago Cubs for prospects Eloy Jiménez, Dylan Cease, Matt Rose, and Bryant Flete.

In July 2020, Quintana underwent surgery to repair a lacerated nerve on his thumb on his throwing arm, which he incurred while washing dishes.

[29] He was activated from the injured list on June 21 and made his return the next day against the San Francisco Giants, and was moved to the bullpen in the process.

[33] After having four no decisions and a loss in his first five games as a Pirate, Quintana earned his first win with the team on May 9, pitching six scoreless innings against the Los Angeles Dodgers, striking out five.

[34] He tossed seven scoreless innings the very next game against the division rival Reds, but was given another no decision as the team failed to score while he was on the field.

[34] On July 29, the Pirates traded Quintana and Chris Stratton to the St. Louis Cardinals for Malcom Núñez and Johan Oviedo.

[34] He made his debut for the Cardinals on August 4 in the second game of a double-header at Busch Stadium, tossing six innings of one-run baseball, and striking out seven.

[39] The Mets announced the following week that additional testing found a benign lesion on his rib and that Quintana would be undergoing surgery which would keep him out until at least July.

The Mets would advance, however, after rallying in the 9th inning with a Pete Alonso 3-run home run to overcome a 0–2 deficit, eventually winning 4–2.

[47][48] During the 2017 Major League Baseball postseason, the Cubs' chartered flight from Washington to Los Angeles had to be diverted to Albuquerque when Quintana's wife fell ill.