Pazos attended and played baseball for Highland High School in Gilbert, Arizona, from which he graduated in 2009. He was second-team All-Region as a sophomore, All-Region as a junior, and All State and Fiesta Region Pitcher of the Year as a senior. He was drafted by the Tampa Bay Rays in the 40th round of the 2009 MLB draft. Pazos did not sign with Tampa Bay. Pazos enrolled at Chandler–Gilbert Community College to play college baseball. He pitched for the Coyotes in 2010, and had a 9–4 win–loss record and a 1.94 earned run average in 95 innings. After one year, he transferred to the University of San Diego to play for the Toreros for the next two seasons. As a sophomore, he was 3–5 with a 3.40 ERA and 41 strikeouts in innings. As a junior, he was 5–1 and had a 2.14 ERA in 63 innings, a WHIP of 0.94, and averaged a strikeout an inning. He was named to the 2012 Rawlings All-West Coast Conference First Team.
The New York Yankees selected Pazos in the 13th round of the 2012 MLB draft, and he signed for a signing bonus of $100,000. He made his professional debut with the Staten Island Yankees of the Class A-Short SeasonNew York-Penn League, going 2–1 with three saves and a 1.79 ERA in 28 relief appearances, with 39 strikeouts in 40.1 innings, and was named a mid-season NYPL All Star. He spent 2013 with Staten Island and the Charleston RiverDogs in the Class ASouth Atlantic League. He pitched to a combined 3–1 record with one save and 33 strikeouts and a 3.93 ERA in innings pitched out of the bullpen. After the season, he played for the Scottsdale Scorpions in the Arizona Fall League, pitching 10.1 innings. Pazos played in 2014 with the Tampa Yankees of the Class A-AdvancedFlorida State League and the Trenton Thunder of the Class AAEastern League. He compiled a combined 0–3 record with 10 saves and a 2.42 ERA with 75 strikeouts in 67 relief innings, averaging 10.1 strikeouts per 9 innings. In 2015, between Trenton and the Scranton/Wilkes-Barre RailRiders of the Class AAAInternational League, he was 3–1 with three saves and a 1.27 ERA, and 49 strikeouts in innings, averaging 10.3 strikeouts per 9 innings. The Yankees promoted Pazos to the major leagues on September 1, and he made his major league debut on September 5. With the Yankees in 2015, he pitched five scoreless innings. In 2016, Pazos split time between the Yankees and the minors. In the minors, pitching primarily for Scranton/Wilkes-Barre, he was 2–2 with one save and a 2.32 ERA, and 47 strikeouts in 31 innings, averaging 13.6 strikeouts per 9 innings. In innings for the Yankees, he gave up five earned runs while winning one game.
Seattle Mariners
The Yankees traded Pazos to the Seattle Mariners for Zack Littell on November 18, 2016. In 2017 with Seattle, he was 4–5 with a 3.86 ERA, as in 53.2 innings he had 65 strikeouts, averaging 10.9 strikeouts per 9 innings. In 2018 with Seattle, he was 4–1 with a 2.88 ERA. In 50 innings in a career-high 60 games he gave up 47 hits and 15 walks, and had 45 strikeouts. He threw a sinker 91.8% of the time, tops in MLB.
On April 26, 2019, Pazos was traded to the Colorado Rockies in exchange for infielder Hunter Stovall. Pitching for the Albuquerque Isotopes in 2019 he was 1-3 with one save and a 8.80 ERA in 39 games. Pitching for the Rockies he was 0-0 with a 1.74 ERA in 12 games.