Interfacing CH3NH3PbI3 (MAPbI3) with 2D van der Waals materials in lateral photodetectors can suppress the dark current and driving voltage, while the interlayer charge separation also renders slower charge dynamics. In this work, we show that more than one order of magnitude faster photoresponse time can be achieved in MAPbI3/MoS2 lateral photodetectors by locally separating the photocharge generation and recombination through a parallel channel of single-layer MAPbI3. Photocurrent (Iph) mapping reveals electron diffusion lengths of about 20 μm in single-layer MAPbI3 and 4 μm in the MAPbI3/MoS2 heterostructure. The illumination-power scaling of Iph and time-resolved photoluminescence studies point to the dominant roles of the heterostructure region in photogeneration and single-layer MAPbI3 in charge recombination. Our results shed new light on the material design that can concurrently enhance photoresponsivity, reduce driving voltage, and sustain high operation speed, paving the path for developing high-performance lateral photodetectors based on hybrid perovskites.