Van der Waals heterostructures consisting of 2D semiconductors and conjugated molecules are of increasing interest because of the prospect of a synergistic enhancement of (opto)electronic properties. In particular, perylenetetracarboxylic dianhydride (PTCDA) on monolayer (ML)-MoS2 has been identified as promising candidate and a staggered type-II energy level alignment and excited state interfacial charge transfer have been proposed. In contrast, it is here found with inverse and direct angle resolved photoelectron spectroscopy that PTCDA/ML-MoS2 supported by insulating sapphire exhibits a straddling type-I level alignment, with PTCDA having the wider energy gap. Photoluminescence (PL) and sub-picosecond transient absorption measurements reveal that resonance energy transfer, i.e., electron–hole pair (exciton) transfer, from PTCDA to ML-MoS2 occurs on a sub-picosecond time scale. This gives rise to an enhanced PL yield from ML-MoS2 in the heterostructure and an according overall modulation of the photoresponse. These results underpin the importance of a precise knowledge of the interfacial electronic structure in order to understand excited state dynamics and to devise reliable design strategies for optimized optoelectronic functionality in van der Waals heterostructures.