Nunez was signed by the Mariners as a sixteen-year-old from Puerto Rico. When he first appeared in the majors in 1982, the eighteen-year-old Nunez became the youngest ever to pitch for the Mariners. Over the next half-dozen seasons Nunez showed sustained periods of excellence between frequent trips to the disabled list.
At the time Seattle traded him to the Mets for Gene Walter midway through the 1988 season, Nunez was third in career saves as a Mariner and fourth in games. He spent the remainder of his career as a fairly effective middle reliever, tossing 75 2/3 innings for the 1993 Oakland Athletics.