Utilization of triplet excitons, which generally emit poorly, is always fundamental to realize highly efficient organic light-emitting diodes (LEDs). While triplet harvest and energy transfer via electron exchange between triplet donor and acceptor are fully understood in doped organic phosphorescence and delayed fluorescence systems, the utilization and energy transfer of triplet excitons in quasi-two-dimensional (quasi-2D) perovskite are still ambiguous. Here, we use an orange-phosphorescence-emitting ultrathin organic layer to probe triplet behavior in the sky-blue-emitting quasi-2D perovskite. The delicate white LED architecture enables a carefully tailored Dexter-like energy-transfer mode that largely harvests the triplet excitons in quasi-2D perovskite. Our white organic-inorganic LEDs achieve maximum forward-viewing external quantum efficiency of 8.6% and luminance over 15 000 cd m-2, exhibiting a significant efficiency enhancement versus the corresponding sky-blue perovskite LED (4.6%). The efficient management of energy transfer between excitons in quasi-2D perovskite and Frenkel excitons in the organic layer opens the door to fully utilizing excitons for white organic-inorganic LEDs.