He pitched in the rookie-level Gulf Coast League for the GCL Dodgers, where he accrued a win-loss record of 6-0 and an earned run average (ERA) of 1.58 in seven games started and 3 relief appearances; he struck out 56 batters in 57 innings.

The Los Angeles organization recognized Núñez as their top minor league pitcher for the month of July.

On August 31, 2006, the Dodgers traded Núñez to the Washington Nationals for veteran utility player Marlon Anderson.

[2] On November 13, 2008, the Yankees traded Núñez, Wilson Betemit, and Jeff Marquez to the Chicago White Sox for Nick Swisher and Kanekoa Texeira.

Nunez retired the Yankees' Johnny Damon, the only batter he faced, on a ground ball to shortstop.