Colloidal quantum dots (CQDs) are emerging as promising materials for constructing infrared sources in view of their tunable luminescence, high quantum efficiency and compatibility with solution processing. However, CQD films available today suffer from a compromise between luminescence efficiency and charge transport, and this leads to unacceptably high power consumption. Here, we overcome this issue by embedding CQDs in a high-mobility hybrid perovskite matrix. The new composite enhances radiative recombination in the dots by preventing transport-assisted trapping losses; yet does so without increasing the turn-on voltage. Through compositional engineering of the mixed halide matrix, we achieve a record electroluminescence power conversion efficiency of 4.9%. This surpasses the performance of previously reported CQD near-infrared devices two-fold, indicating great potential for this hybrid QD-in-perovskite approach.