31,407 || 34–17 |- style="text-align:center;background-color:#ffbbbb" | 52 || May 31 || @ Red Sox || 4 – 3 || Smith (4–1) || Plunk (1–1) || || 33,510 || 34–18 |- style="text-align:center;background-color:#ffbbbb" | 53 || June 2 || Indians || 5–3 || Swindell (6–1) || Moore (6–4) || Jones (12) || 28,052 || 34–19 |- style="text-align:center;background-color:#bbffbb" | 54 || June 3 || Indians || 7–0 || Welch (7–4) || Candiotti (6–3) || || 35,466 || 35–19 |- style="text-align:center;background-color:#bbffbb" | 55 || June 4 || Indians || 4–0 || Stewart (10–2) || Farrell (3–6) || || 34,610 || 36–19 |- style="text-align:center;background-color:#ffbbbb" | 56 || June 5 || Twins || 2–1 || Oliveras (3–2) || C. Young (2–5) || Reardon (9) || 34,320 || 36–20 |- style="text-align:center;background-color:#bbffbb" | 57 || June 6 || Twins || 1–0 || Moore (7–4) || Anderson (6–4) || || 23,505 || 37–20 |- style="text-align:center;background-color:#bbffbb" | 58 || June 7 || Twins || 3–2 || Welch (8–4) || Viola (4–8) || Burns (3) || 27,396 || 38–20 |- style="text-align:center;background-color:#ffbbbb" | 59 || June 9 || @ Rangers || 11–8 || Guante (4–3) || Nelson (1–2) || Russell (14) || 35,799 || 38–21 |- style="text-align:center;background-color:#bbffbb" | 60 || June 10 || @ Rangers || 5–1 || Davis (4–3) || Witt (5–6) || || 40,796 || 39–21 |- style="text-align:center;background-color:#bbffbb" | 61 || June 11 || @ Rangers || 5–1 || Moore (8–4) || Brown (5–3) || Nelson (1) || 32,127 || 40–21 |- style="text-align:center;background-color:#ffbbbb" | 62 || June 12 || @ Royals || 2 – 1 || Gordon (8–2) || Burns (4–1) || || 39,387 || 40–22 |- style="text-align:center;background-color:#ffbbbb" | 63 || June 13 || @ Royals || 5–3 || Appier (1–1) || C. Young (2–6) || Farr (14) || 29,816 || 40–23 |- style="text-align:center;background-color:#bbffbb" | 64 || June 14 || @ Royals || 2–1 || Stewart (11–2) || Leibrandt (4–7) || Honeycutt (5) || 31,087 || 41–23 |- style="text-align:center;background-color:#bbffbb" | 65 || June 16 || @ Orioles || 7–5 || Davis (5–3) || Holton (2–5) || Honeycutt (6) || || 42–23 |- style="text-align:center;background-color:#ffbbbb" | 66 || June 16 || @ Orioles || 5–1 || Tibbs (3–0) || Moore (8–5) || || 40,707 || 42–24 |- style="text-align:center;background-color:#ffbbbb" | 67 || June 17 || @ Orioles || 4–2 || Bautista (3–4) || M. Young (0–1) || Olson (8) || 36,431 || 42–25 |- style="text-align:center;background-color:#ffbbbb" | 68 || June 18 || @ Orioles