The emergence of pathogenic RNA viruses into new hosts can have dramatic consequences for both livestock and public health. Here we characterize the viral genetic changes that were observed in a previous study which experimentally adapted a field isolate of duck influenza virus to swine respiratory cells. Both pre-existing and $de\; novo$ mutations were selected during this adaptation. We compare the $in\; vitro$ growth dynamics of the adapted virus with those of the original strain as well as all possible reassortants using reverse genetics. This full factorial design showed that viral gene segments are involved in complex epistatic interactions on virus fitness, including negative and sign epistasis. We also identify two point mutations at positions 67 and 113 of the HA2 subunit of the hemagglutinin protein conferring a fast growth phenotype on the naïve avian virus in swine cells. These HA2 mutations enhance the pH dependent, HA-mediated membrane fusion. A global H1 maximum-likelihood phylogenetic analysis, combined with comprehensive ancestry reconstruction and tests for directional selection, confirmed the field relevance of the mutation at position 113 of HA2. Most notably, this mutation was associated with the establishment of the H1 ‘avian-like’ swine influenza lineage, regarded as the most likely to cause the next influenza pandemic in humans. This multidisciplinary approach to study the genetics of viral adaptation provides unique insights on the underlying processes leading to influenza emergence in a new host species, and identifies specific targets for future surveillance and functional studies.