Proteins of the green fluorescent protein family represent a convenient experimental model to study evolution of novelty at the molecular level. Here, we focus on the origin of Kaede-like red fluorescent proteins characteristic of the corals of the Faviina suborder. We demonstrate, using an original approach involving resurrection and analysis of the library of possible evolutionary intermediates, that it takes on the order of 12 mutations, some of which strongly interact epistatically, to fully recapitulate the evolution of a red fluorescent phenotype from the ancestral green. Five of the identified mutations would not have been found without the help of ancestral reconstruction, because the corresponding site states are shared between extant red and green proteins due to their recent descent from a dual-function common ancestor. Seven of the 12 mutations affect residues that are not in close contact with the chromophore and thus must exert their effect indirectly through adjustments of the overall protein fold; the relevance of these mutations could not have been anticipated from the purely theoretical analysis of the protein's structure. Our results introduce a powerful experimental approach for comparative analysis of functional specificity in protein families even in the cases of pronounced epistasis, provide foundation for the detailed studies of evolutionary trajectories leading to novelty and complexity, and will help rational modification of existing fluorescent labels.