Wolcott was a key member of the 1995 "Refuse to Lose" Seattle Mariner team, the first Mariner team to reach the playoffs. He was a late season call-up from the minor leagues in August, where he was most impressive in his first MLB start against the Boston Red Sox, the team with which he would pitch his final MLB game in 1999. He started Game 1 of the American League Championship Series vs the Cleveland Indians in 1995 at the age of 22. He walked the bases loaded in the 1st Inning but settled down, scattering 8 hits and 2 runs over 7 innings in a Mariners 3-2 Game 1 win. After his season in NPB, he came back to pitch three games in the Oakland Athletics organization in 2001.