Tin-phthalocyanine molecules adsorbed on Ag(111) were contacted with the tip of a cryogenic scanning tunneling microscope. Orders-of-magnitude variations of the single-molecule junction conductance were achieved by controllably dehydrogenating the molecule and by modifying the atomic structure of the surface electrode. Nonequilibrium Green's function calculations reproduce the trend of the conductance and visualize the current flow through the junction, which is guided through molecule-electrode chemical bonds.