We present new, exact, rotating and accelerating solutions within the framework of five-dimensional Einstein- Gauss-Bonnet theory at the Chern-Simons point. The rotating solutions describe black holes characterized by a single rotation parameter, a mass parameter, and two extra integration constants that can be interpreted as hairs of a gravitational nature. It is noteworthy that the rotation cannot be removed by a large diffeomorphism. We also extend our procedure to dimension seven, providing a new rotating solution with two rotation parameters pertaining to cubic Lovelock theory with a unique vacuum.