| 36 || June 4 || @ Giants || 0–4 || Mark Leiter (3–1) || Tyler Green (4–4) || None || 22,838 || 24–12 |- style="background:#fbb" | 37 || June 5 || @ Padres || 4–5 (10) || Trevor Hoffman (4–1) || Norm Charlton (2–3) || None || 7,233 || 24–13 |- style="background:#fbb" | 38 || June 6 || @ Padres || 0–1 || Fernando Valenzuela (2–2) || Mike Williams (0–1) || Trevor Hoffman (6) || 8,891 || 24–14 |- style="background:#bfb" | 39 || June 7 || @ Padres || 7–1 || Curt Schilling (4–0) || Andy Ashby (2–4) || None || 9,749 || 25–14 |- style="background:#bfb" | 40 || June 9 || @ Dodgers || 4–0 || Paul Quantrill (5–2) || Pedro Astacio (1–4) || None || 29,679 || 26–14 |- style="background:#bfb" | 41 || June 10 || @ Dodgers || 3–0 || Tyler Green (5–4) || Tom Candiotti (2–5) || None || 37,220 || 27–14 |- style="background:#bfb" | 42 || June 11 || @ Dodgers || 2–1 || Mike Mimbs (4–1) || Ramón Martínez (6–4) || Heathcliff Slocumb (15) || 32,223 || 28–14 |- style="background:#fbb" | 43 || June 13 || Astros || 5–6 || Dave Veres (3–1) || Curt Schilling (4–1) || John Hudek (7) || 20,311 || 28–15 |- style="background:#fbb" | 44 || June 14 || Astros || 5–9 || Darryl Kile (2–5) || Norm Charlton (2–4) || Todd Jones (2) || 24,933 || 28–16 |- style="background:#bfb" | 45 || June 15 || Astros || 4–2 || Ricky Bottalico (3–1) || John Hudek (2–2) || None || 29,411 || 29–16 |- style="background:#fbb" | 46 || June 16 || Marlins || 1–2 || Pat Rapp (2–3) || David West (1–1) || Robb Nen (4) || 29,092 || 29–17 |- style="background:#bfb" | 47 || June 17 || Marlins || 11–4 || Mike Mimbs (5–1) || David Weathers (1–3) || None || 37,843 || 30–17 |- style="background:#bfb" | 48 || June 18 || Marlins || 5–3 || Curt Schilling (5–1) || Yorkis Pérez (0–2) || Heathcliff Slocumb (16) || 40,105 || 31–17 |- style="background:#bfb" | 49 || June 19 || @ Mets || 6–3 || Paul Quantrill (6–2) || Dave Mlicki (4–3) || Heathcliff Slocumb (17) || 14,250 || 32–17 |- style="background:#bfb" | 50 || June 20 || @ Mets || 8–2 || Tyler Green (6–4) || Pete Harnisch (1–4) || None || 15,308 || 33–17 |- style="background:#bfb" |