Spin-polarized DFT+U computations have been performed to investigate the role of oxygen vacancies in dissociating H$_2$S on the rutile TiO$_2$(110) surface. A bridged O$_{2c}$ atom is demonstrated to be the most energetically favorable oxygen vacancy site, which makes V(O$_{2c}$) an electron donator center and induces an isolated defect level with narrowed band gaps. A H2S molecule is adsorbed dissociatively over V(O$_{2c}$), but molecularly on the perfect surface. For H$_2$S dissociation, the HS/H intermediate state reveals the best thermal stability on both defected and perfect surfaces. Moreover, potential energy surface analysis shows that V(O$_{2c}$) reduces markedly the energy barriers for the paths along H$_2$S dissociation. This indicates oxygen vacancies to be efficient trap centers for H$_2$S dissociation, as evidenced by a significant interfacial charge transfer promoted by vacancies. This work could provide insights into the role of oxygen vacancies in facilitating the decomposition of H$_2$S on rutile TiO$_2$(110) surface.