The functionality and performance of a semiconductor is determined by its bandgap. Alloying, as for instance in InxGa1-xN, has been a mainstream strategy for tuning the bandgap. Keeping the semiconductor alloys in the miscibility gap (being homogeneous), however, is non-trivial. This challenge is now being extended to halide perovskites - an emerging class of photovoltaic materials. While the bandgap can be conveniently tuned by mixing different halogen ions, as in CsPb(BrxI1-x)3, the so-called mixed-halide perovskites suffer from severe phase separation under illumination. Here, we discover that such phase separation can be highly suppressed by embedding nanocrystals of mixed-halide perovskites in an endotaxial matrix. The tuned bandgap remains remarkably stable under extremely intensive illumination. The agreement between the experiments and a nucleation model suggests that the size of the nanocrystals and the host-guest interfaces are critical for the photo-stability. The stabilized bandgap will be essential for the development of perovskite-based optoelectronics, such as tandem solar cells and full-color LEDs.