London dispersion force is ubiquitous in nature, and is increasingly recognized to be an important factor in a variety of surface processes. Here we demonstrate unambiguously the decisive role of London dispersion force in non-equilibrium growth of ordered nanostructures on metal substrates using aromatic source molecules. Our first-principles based multi-scale modeling shows that a drastic reduction in the growth temperature, from ~1000°C to ~300°C, can be achieved in graphene growth on Cu(111) when the typical carbon source of methane is replaced by benzene or p-Terphenyl. The London dispersion force enhances their adsorption energies by about (0.5-1.8) eV, thereby preventing their easy desorption, facilitating dehydrogenation, and promoting graphene growth at much lower temperatures. These quantitative predictions are validated in our experimental tests, showing convincing demonstration of monolayer graphene growth using the p-Terphenyl source. The general trends established are also more broadly applicable in molecular synthesis of surface-based nanostructures.