Ultraviolet (UV) response of p-Si/i-ZnO/n-ZnO (p-i-n) heterojunction photodetectors (HPDs) was dramatically enhanced by inserting a thin ${\rm SiO}_{\rm x}$ layer to form a ${\rm p}\hbox{-}{\rm Si}/{\rm SiO}_{\rm x}/{\rm i}\hbox{-}{\rm ZnO}/{\rm n}\hbox{-}{\rm ZnO}$ structure. It was found that the leakage current of p-i-n HPDs is largely reduced by about three orders compared with that of conventional p-n HPDs. Photocurrent measurements show that the UV-generated carriers are first accelerated by the electric field in i-ZnO and then tunnel through the thin ${\rm SiO}_{\rm x}$ layer instead of being trapped by the interface states at the p-Si/i-ZnO interface. This increases the UV response and consequently, the UV-to-visible rejection ratio is enhanced from 7 for the p-i-n HPDs without ${\rm SiO}_{\rm x}$ layer to 112 for the HPDs with ${\rm SiO}_{\rm x}$ insertion.