Colloidal gelation is caused by the formation of a percolated network of colloidal particles suspended in a liquid. Thus far the major transport process leading to gelation has been believed to be the brownian diffusion of particles. Contrary to this common belief, we reveal by numerical simulations that many-body hydrodynamic interactions between colloidal particles also play an essential role in gelation: They significantly promote gelation, or lower the colloid volume fraction threshold for percolation, as compared to their absence. We find that the incompressible nature of a liquid component and the resulting self-organization of hydrodynamic flow with a transverse (rotational) character are responsible for this enhancement of network-forming ability.