Sprout suppression is a crucial aspect of maintaining postharvest Solanum tuberosum (potato) tuber quality. 1,4-dimethylnaphthalene (DMN) has demonstrated effective sprout suppression during long-term storage of potatoes. Its mode of action, however, remains unknown, and previous studies utilizing single cultivars preclude identification of a common response to treatment. Thus, the goal of this study was to identify common transcriptomic responses of multiple potato cultivars of varying dormancy lengths to DMN exposure during two dormancy stages. RNA-seq gene expression profiling supported differing sensitivity to DMN treatment dependent upon cultivar and dormancy stage. A limited number of genes with similar expression patterns were common to all cultivars. These were primarily identified in ecodormant tubers and were associated with cell cycle progression, hormone signaling, and biotic and abiotic stress response. DMN treatment resulted in significant upregulation of members of ANAC/NAC and WRKY transcription factor families. Investigation of affected protein-protein interaction networks revealed a small number of networks responsive to DMN in all cultivars. These results suggest that response to DMN is largely cultivar and dormancy stage-dependent, and the primary response is governed by a limited number of stress and growth-related genes and protein-protein interactions.