After signing with the Mariners, Pagán made his professional debut that year with the Pulaski Mariners. He was promoted to the Everett AquaSox in August. In 26.1 relief innings pitched between the two teams he was 1–1 with a 1.03 ERA and 35 strikeouts. In 2014, he pitched for the Clinton LumberKings where he compiled a 2–3 record and 2.89 ERA in 42 relief appearances, and in 2015, he played with the Bakersfield Blaze where he pitched to a 3–8 record and 2.53 ERA. Pagán spent 2016 with the Jackson Generals and Tacoma Rainers, compiling a combined 5–3 record and 2.49 ERA in 65 innings pitched out of the bullpen. Pagán was on Puerto Rico's roster for the 2017 World Baseball Classic. He began the season with Tacoma and was promoted to the major leagues on May 2. On May 3, 2017, he made his major league debut for the Mariners against the Los Angeles Angels of Anaheim at Safeco Field. He was sent down and recalled multiple times during the season before he was recalled for the remainder of the season on July 7. In 34 relief appearances for Seattle, he was 2–3 with a 3.22 ERA, and in 23 appearances for Tacoma, he was 2–1 with a 2.56 ERA.
Oakland Athletics
On November 15, 2017, Pagán was traded to the Oakland Athletics, along with Alexander Campos, for Ryon Healy. He began the season with Oakland, but was sent down to the Nashville Sounds on May 2. He was recalled back to Oakland on May 18.
On December 21, 2018, the Athletics traded Pagán to the Tampa Bay Rays in a three team deal in which the Rays also acquired Rollie Lacy and a competitive balance pick in the 2019 MLB draft, the Athletics acquired Jurickson Profar, and the Texas Rangers acquired Brock Burke, Kyle Bird, Yoel Espinal, Eli White, and $750,000 of international signing bonus pool space. In 2019, after a impressive spring training, Pagán was sent to the Triple-A Durham Bulls. He was recalled on April 16, after Blake Snell fractured his toe. On April 19, Pagán was optioned to Durham when Casey Sadler was recalled, then Pagán was recalled two days later. Pagán later on became the team's closer and finished the season recording 20 saves. He finished with a 2.31 ERA and 96 strikeouts in 70 innings.
San Diego Padres
On February 8, 2020, the Rays traded Pagán to the San Diego Padres in exchange for Manuel Margot and Logan Driscoll.
