The quantum anomalous Hall effect (QAHE) that emerges under broken time-reversal symmetry in topological insulators (TIs) exhibits many fascinating physical properties for potential applications in nanoelectronics and spintronics. However, in transition metal–doped TIs, the only experimentally demonstrated QAHE system to date, the QAHE is lost at practically relevant temperatures. This constraint is imposed by the relatively low Curie temperature (T[subscript c]) and inherent spin disorder associated with the random magnetic dopants. We demonstrate drastically enhanced T[subscript c] by exchange coupling TIs to Tm[subscript 3]Fe[subscript 5]O[subscript 12], a high-T[subscript c] magnetic insulator with perpendicular magnetic anisotropy. Signatures showing that the TI surface states acquire robust ferromagnetism are revealed by distinct squared anomalous Hall hysteresis loops at 400 K. Point-contact Andreev reflection spectroscopy confirms that the TI surface is spin-polarized. The greatly enhanced T[subscript c], absence of spin disorder, and perpendicular anisotropy are all essential to the occurrence of the QAHE at high temperatures.