|| 26,156 || 24–28 |-align="center" bgcolor="bbffbb" | 53 || May 30 || Tigers || 11–7 || Riske (1–2) || Lima (1–3) || || 25,689 || 25–28 |-align="center" bgcolor="bbffbb" | 54 || May 31 || White Sox || 7–0 || Colón (7–3) || Glover (1–1) || || 33,756 || 26–28 |- |-align="center" bgcolor="bbffbb" | 55 || June 1 || White Sox || 8–4 || Báez (5–4) || Ritchie (3–7) || || 37,707 || 27–28 |-align="center" bgcolor="bbffbb" | 56 || June 2 || White Sox || 4–3 || Finley (4–6) || Wright (5–6) || Wickman (13) || 37,760 || 28–28 |-align="center" bgcolor="ffbbbb" | 57 || June 4 || @ Twins || 23–2 || Reed (6–2) || Drese (5–4) || || 14,029 || 28–29 |-align="center" bgcolor="bbffbb" | 58 || June 5 || @ Twins || 6–4 || Sabathia (5–4) || Milton (7–5) || Riske (1) || 15,617 || 29–29 |-align="center" bgcolor="ffbbbb" | 59 || June 6 || @ Twins || 8–3 || Lohse (6–3) || Colón (7–4) || || 15,553 || 29–30 |-align="center" bgcolor="ffbbbb" | 60 || June 7 || Mets || 4–3 || Leiter (6–5) || Báez (5–5) || Benítez (12) || 39,986 || 29–31 |-align="center" bgcolor="ffbbbb" | 61 || June 8 || Mets || 8–6 || Trachsel (4–6) || Finley (4–7) || Benítez (13) || 41,474 || 29–32 |-align="center" bgcolor="bbffbb" | 62 || June 9 || Mets || 8–3 || Drese (6–4) || Estes (2–5) || || 39,436 || 30–32 |-align="center" bgcolor="ffbbbb" | 63 || June 10 || Phillies || 3–1 || Adams (3–4) || Sabathia (5–5) || Mesa (18) || 28,440 || 30–33 |-align="center" bgcolor="bbffbb" | 64 || June 11 || Phillies || 5–1 || Colón (8–4) || Wolf (3–5) || Wickman (14) || 30,238 || 31–33 |-align="center" bgcolor="ffbbbb" | 65 || June 12 || Phillies || 7–3 || Padilla (9–4) || Paronto (0–1) || || 35,783 || 31–34 |-align="center" bgcolor="bbffbb" | 66 || June 13 || Orioles || 2–1 (10) || Riggan (1–0) || Roberts (3–2) || || 26,745 || 32–34 |-align="center" bgcolor="bbffbb" | 67 || June 14 || @ Rockies || 5–3 || Drese (7–4) || Thomson (6–6) || Wickman (15) || 40,156 || 33–34 |-align="center" bgcolor="ffbbbb" | 68 || June 15 || @ Rockies || 7–4 || Jones (1–1) || Paronto (0–2) || Jimenez (18) || 41,870 || 33–35 |-align="center" bgcolor="bbffbb" | 69 || June 16 || @ Rockies || 5–4 || Colón (9–4) || Neagle (4–4)