In the giant-impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however, the current lunar orbital inclination of five degrees requires a subsequent dynamical process that is still unclear^{1, 2, 3}. In addition, the giant-impact theory has been challenged by the Moon’s unexpectedly Earth-like isotopic composition^{4, 5}. Here we show that tidal dissipation due to lunar obliquity was an important effect during the Moon’s tidal evolution, and the lunar inclination in the past must have been very large, defying theoretical explanations. We present a tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modelling, we show that the solar perturbations on the Moon’s orbit naturally induce a large lunar inclination and remove angular momentum from the Earth–Moon system. Our tidal evolution model supports recent high-angular-momentum, giant-impact scenarios to explain the Moon’s isotopic composition^{6, 7, 8} and provides a new pathway to reach Earth’s climatically favourable low obliquity.