In July 1960, Bob Gibson and Sandy Koufax were struggling 24-year-old pitchers.
Koufax had a 3-8 record for the Dodgers. Gibson was 1-2 for the Cardinals. Both had been tried as starters and were deemed to be too inconsistent.
After pitching a one-hitter against the Pirates on May 23, 1960, Koufax lost his next four decisions and his ERA rose to 4.64. In a July 4, 1960, start against the Cardinals at St. Louis, Koufax faced six batters, got one out and was lifted.
Gibson opened the 1960 season with the Cardinals, but was sent to the minors in May before he was brought back a month later. On July 6, 1960, Gibson started against the Cubs and gave up four runs in 2.1 innings, raising his ERA for the season to 6.00.
Banished to bullpen
On July 10, 1960, for the only time in their Hall of Fame careers, Gibson and Koufax appeared in the same game as relievers. Their dual relief appearance took place at the Los Angeles Memorial Coliseum on a Saturday afternoon.
Koufax was on a short hook; Gibson was used as a mop-up man.
Ron Kline started for the Cardinals and Stan Williams for the Dodgers but neither was effective.
Koufax entered in the seventh to protect a 7-6 lead. Ken Boyer reached on an error by third baseman Jim Gilliam and Daryl Spencer walked. Out came Koufax, replaced by Ed Roebuck. Boyer stole third and scored on George Crowe’s sacrifice fly, tying the score at 7-7. Koufax was charged with an unearned run.
The Dodgers regained the lead, 8-7, with a run off Bob Duliba in the bottom of the seventh. Duliba gave up three more runs in the eighth. With one out and runners on first and second, the Cardinals turned to Gibson. He struck out Maury Wills looking and retired Roebuck on a groundout. The Dodgers won, 11-7. Boxscore
On the rise
Koufax finished the season with an 8-13 record, appearing in 37 games (26 starts). Gibson went 3-6 in 27 appearances (12 starts).
From then on, whenever they faced one another, it was as starters who were considered the best in the business.
RetroSimba 
Interesting. I hated listening to the games on KMOX when Sandy started, even when Gibby was out there for us!
I can imagine how tough it was to face Sandy Koufax. Always was amazed how well Charlie James did against him: https://retrosimba.com/2012/08/31/gibson-vs-koufax-a-grand-game-for-charlie-james/
I seem to remember a season when Koufax beat Gibby in back to back 1-0 starts, one in LA and one in Stl. Tommy Davis hit a home run in each game for the only runs. Both pitchers were masterful.
Thanks, your memory is pretty good. I searched the box scores from 1959 through 1966 and, unless I missed something, there were 2 times when Sandy Koufax beat Bob Gibson in 1-0 games. The first was May 25, 1961, and the second was June 18, 1962. Both times, Tommy Davis produced the run with a home run against Gibson.
I remember that too! Pretty sure it was ’65 or ’66