Evolutionary adaptation to new environments likely results from a combination of selective sweeps and polygenic shifts, depending on the genetic architecture of traits under selection. While selective sweeps have been widely studied, polygenic responses are considered more prevalent but challenging to quantify. The infinitesimal model makes explicit the hypothesis about the dynamics of changes in allele frequencies under selection, where only allelic effect sizes, frequencies, linkage, and gametic disequilibrium matter. Departures from this, like long-range correlations of allele frequency changes, could be a signal of epistasis in polygenic response. We performed an Evolve & Resequence experiment in Drosophila melanogaster exposing flies to a high sugar diet as a source of environmental stress for over 100 generations. We tracked allele frequency changes in >3000 individually sequenced flies as well as population pools and searched for loci under selection by identifying sites with allele frequency trajectories that differentiated selection regimes consistently across replicates. We estimate that at least 4% of the genome was under positive selection, the result of a highly polygenic response. Most of this response was seen as small but consistent allele frequency changes over time, and there were only a few large allele-frequency changes (selective sweeps). We then searched for signatures of selection on pairwise combinations of alleles in the new environment and found several strong signals of putative epistatic interactions across unlinked loci that were consistent across selected populations. Finally, we measured differentially expressed genes (DEGs) across treatments and show that DEGs are enriched for selected SNPs, suggesting a regulatory basis for the selective response. Our results suggest that epistatic contributions to polygenic selective response are common and lead to detectable signatures.