Potato is one of the most important vegetable crops worldwide. Its growth, development and ultimately yield is hindered by drought stress condition. Breeding and selection of deep-rooted and drought-tolerant potato varieties has become a prime approach for improving the yield and quality of potato (Solanum tuberosum L.) in arid and semiarid areas. A comprehensive understanding of root development-related genes has enabled scientists to formulate strategies to incorporate them into breeding to improve complex agronomic traits and provide opportunities for the development of stress tolerant germplasm. Root response to drought stress is an intricate process regulated through complex transcriptional regulatory network. To understand the rooting depth and molecular mechanism, regulating root response to drought stress in potato, transcriptome dynamics of roots at different stages of drought stress were analyzed in deep (C119) and shallow-rooted (C16) cultivars. Stage-specific expression was observed for a significant proportion of genes in each cultivar and it was inferred that as compared to C16 (shallow-rooted), approximately half of the genes were differentially expressed in deep-rooted cultivar (C119). In C16 and C119, 11 and 14 coexpressed gene modules, respectively, were significantly associated with physiological traits under drought stress. In a comparative analysis, some modules were different between the two cultivars and were associated with differential response to specific drought stress stage. Transcriptional regulatory networks were constructed, and key components determining rooting depth were identified. Through the results, we found that rooting depth (shallow vs deep) was largely determined by plant-type, cell wall organization or biogenesis, hemicellulose metabolic process, and polysaccharide metabolic process. In addition, candidate genes responding to drought stress were identified in deep (C119) and shallow (C16) rooted potato varieties. The results of this study will be a valuable source for further investigations on the role of candidate gene(s) that affect rooting depth and drought tolerance mechanisms in potato.