|| @ Tigers || 4–0 || Morton (7–0) || Turnbull (3–5) || — || 14,272 || 36–23 || W1 |-style="background:#bfb" | 60 || June 6 || @ Tigers || 6–1 || Beeks (5–0) || Norris (2–5) || — || 21,442 || 37–23 || W2 |-style="background:#bfb" | 61 || June 7 || @ Red Sox || 5–1 || Chirinos (7–2) || Porcello (4–6) || — || 36,803 || 38–23 || W3 |-style="background:#bfb" | 62 || June 8 || @ Red Sox || 9–2 || Yarbrough (5–2) || Smith (0–2) || — || 35,564 || 39–23 || W4 |-style="background:#fbb" | 63 || June 8 || @ Red Sox || 1–5 || Price (4–2) || Poche (0–1) || — || 37,048 || 39–24 || L1 |-style="background:#bfb" | 64 || June 9 || @ Red Sox || 6–1 || Snell (4–5) || Rodríguez (6–4) || — || 34,643 || 40–24 || W1 |-style="background:#bfb" | 65 || June 10 || Athletics || 6–2 || Morton (8–0) || Anderson (0–1) || — || 16,091 || 41–24 || W2 |-style="background:#fbb" | 66 || June 11 || Athletics || 3–4 || Fiers (6–3) || Pagán (1–1) || Treinen (15) || 11,132 || 41–25 || L1 |-style="background:#fbb" | 67 || June 12 || Athletics || 2–6 || Hendriks (3–0) || Kolarek (2–2) || — || 17,946 || 41–26 || L2 |-style="background:#fbb" | 68 || June 13 || Angels || 3–5 || Skaggs (5–6) || Yarbrough (5–3) || Bedrosian (1) || 15,291 || 41–27 || L3 |-style="background:#bfb" | 69 || June 14 || Angels || 9–4 || Pagán (2–1) || Buttrey (4–3) || — || 21,598 || 42–27 || W1 |-style="background:#fbb" | 70 || June 15 || Angels || 3–5 || Suárez (2–1) || Morton (8–1) || Robles (10) || 22,320 || 42–28 || L1 |-style="background:#bfb" | 71 || June 16 || Angels || 6–5 || Poche (1–1) || Canning (2–3) || Castillo (7) || 20,508 || 43–28 || W1 |-style="background:#fbb" | 72 || June 17 || @ Yankees || 0–3 || Tanaka (5–5) || Chirinos (7–3) || — || 39,042 || 43–29 || L1 |-style="background:#fbb" | 73 || June 18 || @ Yankees || 3–6 || Happ (7–3) || Roe (0–3) || Chapman (19) || 40,479 || 43–30 || L2 |-style="background:#fbb" | 74 || June 19 || @ Yankees || 1–12 || Sabathia (4–4) || Snell (4–6) || — || 41,144 || 43–31 || L3 |-style="background:#fbb" | 75 ||