We conduct three-dimensional hydrodynamical simulations of hypervelocity impacts into the crust of Titan to determine the fraction of liquid water generated, under the reasonable assumption that the crust is largely water ice, and to track the fate of the organic-rich layer that is thought to overlie the ice over much of the surface. Impactors larger than a kilometer in diameter are only slightly affected by the atmosphere, while those well under that size are strongly decelerated and broken up before reaching the surface. Impact of a 2 km diameter icy projectile into the crust at velocities of 7 km per second or higher, and angles of impact between 30° and 45°, generate about 2-5% melt by volume within the crater. Our results for the amount of aqueous melt generated in impacts on Titan are broadly consistent with the analytic model developed by Thompson and Sagan (1992) although our numerical model allows us to more precisely quantify the fraction of melt, and fate of the organics, as a function of the impact parameters. While much of the organic surface layer is heavily shocked and ejected from the immediate region of the crater, a significant fraction located behind the oblique impact trajectory is only lightly shocked and is deposited in the liquid water at the crater base. Simple calculations suggest that the resulting aqueous organic phase may remain liquid for hundreds of years or longer, enough time for the synthesis of simple precursor molecules to the origin of life.