|| Rays || 9–6 || Carpenter (1–2) || Snell (3–5) || Greene (19) || 15,420 || 23–34 || W1 |- bgcolor="ffbbbb | 58 || June 5 || Rays || 0–4 || Morton (7–0) || Turnbull (3–5) || — || 14,272 || 23–35 || L1 |- bgcolor="ffbbbb | 59 || June 6 || Rays || 1–6 || Beeks (5–0) || Norris (2–5) || — || 21,442 || 23–36 || L2 |- bgcolor="ffbbbb | 60 || June 7 || Twins || 3–6 || Harper (1–0) || Jiménez (2–4) || Parker (9) || 21,551 || 23–37 || L3 |- bgcolor="bbffbb | 61 || June 8 || Twins || 9–3 || Ramirez (2–0) || Gibson (6–3) || — || 26,818 || 24–37 || W1 |- bgcolor="ffbbbb | 62 || June 9 || Twins || 2–12 || Odorizzi (9–2) || Carpenter (1–3) || — || 20,127 || 24–38 || L1 |- bgcolor="ffbbbb | 63 || June 11 || @ Royals || 2–3 || Barlow (2–2) || Alcántara (2–1) || Kennedy (5) || 20,776 || 24–39 || L2 |- bgcolor="bbffbb | 64 || June 12 || @ Royals || 3–2 || Ramirez (3–0) || Diekman (0–3) || Greene (20) || 19,870 || 25–39 || W1 |- bgcolor="ffbbbb | 65 || June 13 || @ Royals|| 3–7 || Bailey (5–6) || Boyd (5–5) || Kennedy (6) || 25,454 || 25–40 || L1 |- bgcolor="ffbbbb | 66 || June 14 || Indians || 4–13 || Plutko (3–1) || Carpenter (1–4) || — || 22,362 || 25–41 || L2 |- bgcolor="ffbbbb | 67 || June 15 || Indians || 2–4 || Bieber (6–2) || Ramirez (3–1) || Hand (20) || 25,523 || 25–42 || L3 |- bgcolor="ffbbbb | 68 || June 16 || Indians || 0–8 || Bauer (5–6) || Turnbull (3–6) || — || 26,705 || 25–43 || L4 |- bgcolor="bbffbb | 69 || June 18 || @ Pirates || 5–4 || Farmer (4–4) || Crick (2–3) || Greene (21) || 18,301 || 26–43 || W1 |- bgcolor="ffbbbb | 70 || June 19 || @ Pirates || 7–8 || Rodríguez (2–3) || Ramirez (3–2) || Vázquez (17) || 18,088 || 26–44 || L1 |- bgcolor="ffbbbb | 71 || June 21 || @ Indians || 6–7 || Cimber (3–2) || Jiménez (2–5) || Hand (21) || 30,717 || 26–45 || L2 |- bgcolor="ffbbbb | 72 || June 22 || @ Indians || 0–2 || Civale (1–0) || Turnbull (3–7)