In 1992, with the support of his father, at the time a part of the Dallas Cowboys scouting department, Garrett was signed as a free agent. He was released on August 31 and later signed to the team's practice squad. In 1993, his preseason performances allowed him to make the team as the third-string quarterback behind Troy Aikman and Hugh Millen. He eventually passed Millen on the depth chart. In the eighth game of the season, after Aikman injured his left hamstring against the New York Giants in the third quarter, Garrett finished the game, completing 5 of 6 passes for 34 yards and leading 2 touchdown drives. He was named the starter for the next game against the Phoenix Cardinals, where he completed 2 of 6 passes for 25 yards and helped the team score on a field goal, before being replaced on the third series in favor of Bernie Kosar, who had been signed 4 days earlier. Kosar became the backup quarterback for the rest of the season after the game.