The distinctive electronic structure found at interfaces between materials can allow unconventional quantum states to emerge. Here we report on the discovery of superconductivity in electron gases formed at interfaces between (111)-oriented KTaO3 and insulating overlayers of either EuO or LaAlO3. The superconducting transition temperature, as high as 2.2 kelvin, is about one order of magnitude higher than that of the LaAlO3/SrTiO3 system. Notably, similar electron gases at KTaO3 (001) interfaces remain normal down to 25 millikelvin. The critical field and current-voltage measurements indicate that the superconductivity is two-dimensional. In EuO/KTaO3 (111) samples, a spontaneous in-plane transport anisotropy is observed before the onset of superconductivity, suggesting the emergence of a distinct "stripe"-like phase, which is also revealed near the critical field.