We investigate the tunneling properties of a two-species few-boson mixture in a one-dimensional triple well and harmonic trap. The mixture is prepared in an initial state with a strong spatial correlation for one species and complete localization of the other species. We observe a correlation-induced tunneling process in the weak interspecies interaction regime. The onset of the interspecies interaction disturbs the spatial correlations of one species and induces a tunneling process between the correlated wells. The corresponding tunneling properties can be controlled by the spatial correlations with an underlying mechanism that is inherently different from the well-known resonant tunneling process. We also observe and analyze the correlated tunneling of both species in the intermediate interspecies interaction regime and the tunneling via higher band states for strong interactions.