The conductance of a molecular junction is commonly determined by either charge-transfer doping, where alignment of the Fermi energy to the molecular levels is achieved, or tunnelling through the tails of molecular resonances within the highest-occupied and lowest-unoccupied molecular-orbital gap. Here, we present an alternative mechanism where electron transport is dominated by electrode surface states. They give rise to metallization of the molecular bridge and additional, pronounced conductance resonances allowing for substantial tailoring of its electronic properties via, e.g., a gate voltage. This is demonstrated in a field-effect geometry of a fullerene bridge between two metallic carbon nanotubes.