"How Krypto Made History!" from Superboy #75 is really the first Krypto solo story, and though Superboy appears, HE'S actually the guest-star. It begins with a game of tag between the two Kryptonians, ending when, chasing each other through the Earth's crust, Krypto gives up on the game to retrieve a dinosaur bone. But yuck, it's turned!
In Adventure Comics #264's "The Helpless Hero", Krypto stays in the objective present to help his master when the Teen of Steel's powers go awry. To help oil drillers (Superboy, oil lobby shill) without the villain distorting his powers, Clark secretly calls Krypto to bore a hole in his place. But the tricky Zall-Dix can affect Krypto's abilities too!