Tailored intense laser fields can be used to steer electron and nuclear dynamics in molecules and control chemical reactions. Here we demonstrate that inhomogeneous nanoscopic near fields provide an additional mechanism for controlling light-induced chemical reactions. This is investigated by quantum-dynamical calculations on dissociation of H2+ in few-cycle near fields with a controlled carrier-envelope phase. Directional dissociation asymmetry analysis reveals that the spatial asymmetry of the field is critical in controlling and in modifying field-induced dissociation pathways such as zero-photon dissociation, bond softening, and above-threshold dissociation. The degree of impact strongly depends on the maximum length scale of coherent control in a dissociation channel. The results pave the way towards coherent control of molecular reactions in a wide range of molecules in inhomogeneous near fields.