Sweet potato (Ipomoea batatas [L.] Lam) is a nutrient-dense food crop with productivity constraints imposed by drought stress in agricultural ecosystems. Accelerated climatic changes could further reduce the cultivated area and result in significant yield decline. Molecular regulatory mechanisms underlying adaptive responses to abiotic have not been well-characterized for I. batatas due to high ploidy and lack of a high-quality reference sequence. Identification of candidate genes involved in transcriptional response to drought is critical for developing new stress tolerant varieties through genetic engineering. A comparative genomic analysis was conducted to understand regulatory mechanisms underlying adaptive response to drought stress in I. batatas. The differential response to drought-stress was assessed for two popular cultivars (Bauregard and Haterras) at three development timepoints in leaf and for storage root tissues. Using I. batatas progenitor genomic resources, differentially expressed genes (DEGs) identified in the analysis were functionally annotated to understand their potential roles in regulating adaptive responses to drought stress. Differential expression analyses identified 27,976 significantly differentially expressed genes across the two genotypes, two tissues and four time points. We mapped 3,127 I. trifida and I. triloba genes orthologous to annotated plant TFs. Several WRKY, NAC, and MYB TFs were upregulated in drought stress in leaves and control transcription dynamics. 1,432 genes mapped to I. trifida and I. triloba were identified as kinases. Among these, several AGC, CDPK, MAPK, and PERK protein kinases were significantly differentially expressed across multiple comparisons, suggesting stress-related signaling activity. TF and kinase orthologs with high expression changes at multiple time points in I. batatas drought stress response was mapped on A. thaliana transcriptional and signaling pathways. Other categories of differentially expressed enzymes involved in photosynthesis, kinase activity, signal transduction, and response to cold and DNA-binding transcription factor activity were analyzed for their drought stress role. This study contributes regulatory genomics analyses on genes and metabolites associated with drought resistance, providing new insights into the molecular mechanisms of drought tolerance in sweet potato.