Semiconductor photoconductive switches are useful and versatile emitters of terahertz (THz) radiation with a broad range of applications in THz imaging and time-domain spectroscopy. One fundamental challenge for achieving efficient ultrafast switching, however, is the relatively long carrier lifetime in most common semiconductors. To obtain picosecond ultrafast pulses, especially when coupled with waveguides/transmission lines, semiconductors are typically engineered with high defect density to reduce the carrier lifetimes, which in turn lowers the overall power output of the photoconductive switches. To overcome this fundamental trade-off, here we present a new hybrid photoconductive switch design by engineering a hot-carrier fast lane using graphene on silicon. While photoexcited carriers are generated in the silicon layer, similar to a conventional switch, the hot carriers are transferred to the graphene layer for efficient collection at the contacts. As a result, the graphene-silicon hybrid photoconductive switch emits THz fields with up to 80 times amplitude enhancement compared to its graphene-free counterpart. These results both further the understanding of ultrafast hot carrier transport in such hybrid systems and lay the groundwork toward intrinsically more powerful THz devices based on 2D-3D hybrid heterostructures.