Here’s another oddity (or two of them) that I remember as a kid:
On September 17, 1968, Gaylord Perry, then with the Giants, no-hit the Cardinals. On September 18, Ray Washburn of the Cardinals returned the favor against the Giants. First time that had ever happened.
On April 30, 1969, Jim Maloney of the Reds no-hit the Astros. On May 1, Don Wilson of the Astros no-hit the Reds.