|- style="background:#fbb" | 55 || June 12 || Giants || 0–3 || Mike McCormick (4–5) || Jack Meyer (4–3) || None || 20,595 || 21–34 |- style="background:#fbb" | 56 || June 13 || Giants || 1–2 || Johnny Antonelli (9–3) || Ray Semproch (2–5) || None || 18,941 || 21–35 |- style="background:#bfb" | 57 || June 14 || Giants || 7–5 || Humberto Robinson (2–0) || Sam Jones (7–6) || None || || 22–35 |- style="background:#bfb" | 58 || June 14 || Giants || 6–3 || Robin Roberts (5–5) || Stu Miller (3–3) || None || 21,562 || 23–35 |- style="background:#fbb" | 59 || June 16 || @ Cardinals || 1–8 || Vinegar Bend Mizell (8–3) || Rubén Gómez (1–4) || None || || 23–36 |- style="background:#fbb" | 60 || June 16 || @ Cardinals || 2–5 || Ernie Broglio (1–5) || Jim Owens (4–4) || Lindy McDaniel (4) || 17,068 || 23–37 |- style="background:#fbb" | 61 || June 17 || @ Cardinals || 4–10 || Marshall Bridges (1–0) || Humberto Robinson (2–1) || None || 16,765 || 23–38 |- style="background:#bfb" | 62 || June 19 || @ Cubs || 8–7 || Gene Conley (4–3) || Bob Anderson (3–6) || Jim Owens (1) || 8,516 || 24–38 |- style="background:#bfb" | 63 || June 20 || @ Cubs || 6–3 || Robin Roberts (6–5) || Dick Drott (1–1) || None || 13,557 || 25–38 |- style="background:#fbb" | 64 || June 21 || @ Cubs || 0–4 || John Buzhardt (4–2) || Rubén Gómez (1–5) || None || 17,995 || 25–39 |- style="background:#fbb" | 65 || June 22 || @ Dodgers || 2–6 || Sandy Koufax (4–1) || Jim Owens (4–5) || None || 10,290 || 25–40 |- style="background:#fbb" | 66 || June 23 || @ Dodgers || 3–4 || Danny McDevitt (6–6) || Gene Conley (4–4) || None || 11,978 || 25–41 |- style="background:#fbb" | 67 || June 24 || @ Dodgers || 6–9 || Roger Craig (2–0) || Don Cardwell (1–5) || Clem Labine (7) || 17,315 || 25–42 |- style="background:#fbb" | 68 || June 25 || @ Dodgers || 2–5 || Don Drysdale (8–5) || Robin Roberts (6–6) || None || 14,662 || 25–43 |- style="background:#fbb" | 69 || June 26 || @ Giants || 0–8 || Mike McCormick (6–7) || Jim Owens (4–6) || None || 15,816 || 25–44 |- style="background:#bfb" | 70 || June 27 || @