In his first three seasons with the Blue Jays, he went a combined 40–11 with a 3.28 ERA, and the team made the playoffs all three years, including World Series wins in 1992 and 1993. Guzman won two games in both the 1992 and 1993 ALCS but was not able to secure a win in either World Series. His playoff record was 5–1 in eight starts with a 2.44 ERA.
Guzman had an ERA of 2.93 in 1996, which was the lowest in the American League among qualified pitchers.
Guzman possessed a very good fastball and strikeout ability, striking out 7.5 batters per nine innings during his career. On the mound, he worked very deliberately and was one of the slower working pitchers in the game, earning him the nickname "Human Rain Delay" from Toronto fans. He led the American league in wild pitches in 1993 and 1994.