Quantum dots (QDs) are semiconductor nanocrystals whose optical properties can be tuned by altering their size. By combining QDs with dyes we can make hybrid QD-dye systems exhibiting energy transfer (ET) between QDs and dyes, which is important in sensing and lighting applications. In conventional QDs that need a shell to passivate surface defects, ET usually proceeds through Förster resonance energy transfer (FRET) that requires significant spectral overlap between QD emission and dye absorbance, as well as large oscillator strengths of those transitions. This considerably limits the choice of dyes. In contrast, perovskite QDs do not require passivating shells for bright emission, which makes ET mechanisms beyond FRET accessible. This work explores the design of a CsPbBr3 QD-dye system to achieve efficient ET from CsPbBr3 QDs to dyes with dimethyl iminium binding groups where the close binding of dyes surface facilitates spatial wavefunction overlap. Using steady-state and time-resolved photoluminescence experiments, we demonstrate that efficient ET from CsPbBr3 to dyes with minimal spectral overlap proceeds via the Dexter exchange-type mechanism, which overcomes the conventional restriction of spectral overlap that severely limits the tunability of these systems. This approach opens new avenues for QD-molecule hybrids for a wide range of applications.