Electronic structure and carrier behavior in semiconductor junctions can be effectively modulated on the application of strain. This work represents the first demonstration of a large-area, flexible, paper-based graphene-molybdenum disulfide (Gr/MoS2) broadband photodetector using a low-cost solution-processed hydrothermal method and enhancement in photodetection through strain modulation by assembling the device on polydimethylsiloxane. Optimization, in terms of process parameters, was carried out to obtain trilayer MoS2 over Gr-cellulose paper. Under strain, potential barrier variation and piezopotential induced in MoS2 leads to 79.41% enhancement in photodetection in the visible region. Piezopotential induced in MoS2 lowers the conduction-band energy thereby increasing the effective electric field favoring easy electron-hole separation. The advantage of vertically stacked Gr/MoS2 for the photodetector is the utilization of the entire area as a junction where effective separation of electron-hole pairs occurs. Detailed studies of the mechanism in terms of potential barrier variation in Gr/MoS2 and an energy-band diagram are presented to help understand the proposed phenomenon. The present work demonstrates the significance of few-layer MoS2 or Gr in relation to strain-modulated photosensing in comparison to their counterparts grown via chemical vapor deposition. The results provide an excellent approach for the fabrication of low-cost heterojunctions for improved optoelectronic performance, which can be further extended to similar 2D-material heterojunctions for analog, digital and optoelectronic applications. © 2017 IOP Publishing Ltd.