13,616 || 26–25 |- style="background:#fbb" | 52 || June 3 || Giants || 4–7 || Jerry Spradlin (1–1) || Curt Schilling (8–3) || Robb Nen (16) || 20,560 || 26–26 |- style="background:#bfb" | 53 || June 4 || @ Orioles || 9–5 || Chad Ogea (3–3) || Scott Erickson (1–8) || None || 47,542 || 27–26 |- style="background:#fbb" | 54 || June 5 || @ Orioles || 6–7 (10) || Mike Timlin (2–4) || Steve Montgomery (0–2) || None || 48,531 || 27–27 |- style="background:#bfb" | 55 || June 6 || @ Orioles || 11–7 || Joel Bennett (2–1) || Ricky Bones (0–2) || None || 47,833 || 28–27 |- style="background:#bfb" | 56 || June 7 || Yankees || 6–5 || Paul Byrd (8–3) || Andy Pettitte (3–4) || None || 37,180 || 29–27 |- style="background:#bfb" | 57 || June 8 || Yankees || 11–5 || Yorkis Pérez (3–1) || Jason Grimsley (5–1) || None || 44,444 || 30–27 |- style="background:#fbb" | 58 || June 9 || Yankees || 5–11 || David Cone (6–2) || Chad Ogea (3–4) || None || 42,047 || 30–28 |- style="background:#bfb" | 59 || June 11 || Blue Jays || 8–4 || Randy Wolf (1–0) || Joey Hamilton (0–4) || None || 26,541 || 31–28 |- style="background:#bfb" | 60 || June 12 || Blue Jays || 7–2 || Paul Byrd (9–3) || Kelvim Escobar (5–4) || None || 20,449 || 32–28 |- style="background:#fbb" | 61 || June 13 || Blue Jays || 2–7 || Pat Hentgen (5–5) || Curt Schilling (8–4) || None || 28,459 || 32–29 |- style="background:#fbb" | 62 || June 15 || @ Padres || 1–6 || Matt Clement (2–7) || Chad Ogea (3–5) || None || 16,134 || 32–30 |- style="background:#bfb" | 63 || June 16 || @ Padres || 4–2 || Randy Wolf (2–0) || Sterling Hitchcock (4–6) || Wayne Gomes (6) || 15,136 || 33–30 |- style="background:#bfb" | 64 || June 17 || @ Padres || 7–5 || Paul Byrd (10–3) || Woody Williams (2–5) || Wayne Gomes (7) || 16,671 || 34–30 |- style="background:#bfb" | 65 || June 18 || @ Dodgers || 2–1 || Curt Schilling (9–4) || Ismael Valdez (5–6) || Wayne Gomes (8) || 41,590 || 35–30 |- style="background:#fbb" | 66 || June 19 || @ Dodgers || 1–8 || Darren Dreifort (6–5) || Robert Person (0–3) || None || 32,315 || 35–31 |- style="background:#fbb"