The development of low-resistance source/drain contacts to transition-metal dichalcogenides (TMDCs) is crucial for the realization of high-performance logic components. In particular, efficient hole contacts are required for the fabrication of p-type transistors with MoS2, a model TMDC. Previous studies have shown that the Fermi level of elemental metals is pinned close to the conduction band of MoS2, thus resulting in large Schottky barrier heights for holes with limited hole injection from the contacts. Here, we show that substoichiometric molybdenum trioxide (MoOx, x < 3), a high work function material, acts as an efficient hole injection layer to MoS2 and WSe2. In particular, we demonstrate MoS2 p-type field-effect transistors and diodes by using MoOx contacts. We also show drastic on-current improvement for p-type WSe2 FETs with MoOx contacts over devices made with Pd contacts, which is the prototypical metal used for hole injection. The work presents an important advance in contact engineering of TMDCs and will enable future exploration of their performance limits and intrinsic transport properties.