|| W2 |- style="background:#cfc;" | 57 || June 2 || Royals || 5–1 || Sampson (4–3) || Keller (3–7) || — || 21,891 || 30–27 || W3 |- style="background:#fbb;" | 58 || June 4 || Orioles || 11–12 || Bundy (3–6) || Smyly (1–4) || Givens (5) || 21,903 || 30–28 || L1 |- style="background:#cfc;" | 59 || June 5 || Orioles || 2–1 (12) || Springs (3–1) || Fry (0–3) || — || 21,163 || 31–28 || W1 |- style="background:#cfc;" | 60 || June 6 || Orioles || 4–3 || Jurado (3–2) || Hess (1–8) || Kelley (7) || 20,462 || 32–28 || W2 |- style="background:#fbb;" | 61 || June 7 || Athletics || 3–5 ||Petit (1–1) ||Leclerc (1–2) || Treinen (13) || 25,120 || 32–29 || L1 |- style="background:#cfc;" | 62 || June 8 (1) || Athletics || 10–5 ||Springs (4–1) || Blackburn (0–1) || — || 22,327 || 33–29 ||W1 |- style="background:#cfc;" | 63 || June 8 (2) || Athletics || 3–1 || Sampson (5–3) || Bassitt (3–2) || — || 39,514 || 34–29 || W2 |- style="background:#fbb;" | 64 || June 9 || Athletics || 8–9 || Montas (8–2) || Smyly (1–5) || Treinen (14) || 20,358 || 34–30 || L1 |- style="background:#cfc;" | 65 || June 10 || @ Red Sox || 4–3 (11) || Chavez (2–1) || Brasier (2–3) || Martin (2) || 34,422 || 35–30 || W1 |- style="background:#cfc;" | 66 || June 11 || @ Red Sox || 9–5 || Jurado (4–2) || Hernández (0–1) || — || 35,121 || 36–30 || W2 |- style="background:#fbb;" | 67 || June 12 || @ Red Sox || 3–4 || Barnes (3–1) || Chavez (2–2) || — || 34,330 || 36–31 || L1 |- style="background:#fbb;" | 68 || June 13 || @ Red Sox || 6–7 || Workman (4–1) || Fairbanks (0–1) || Smith (1) || 35,841 || 36–32 || L2 |- style="background:#cfc;" | 69 || June 14 || @ Reds || 7–1 || Martin (1–0) || Mahle (2–7) || Smyly (1) || 30,090 || 37–32 || W1 |- style="background:#cfc;" | 70 || June 15 || @ Reds || 4–3 || Minor (6–4) || Roark (4–6) || Kelley (8) || 25,693 || 38–32 || W2 |- style="background:#fbb;" | 71 || June 16 || @ Reds || 3–11 || Gray (3–5) || Jurado (4–3) || — || 24,079 || 38–33 || L1 |- style="background:#cfc;" | 72