Glutathione S-transferases (GSTs) play crucial roles in crop stress tolerance through protection against oxidative damage. In this study, we conducted genome-wide identification and expression analysis of the GST gene family in the autotetraploid potato cultivar Cooperative-88 (C88) using bioinformatic approaches. We identified 366 GST genes in the potato genome, which were classified into 10 subfamilies. Chromosomal mapping revealed that StGSTs were distributed across all 12 chromosomes, with 13 tandem duplication events observed in three subfamilies. Analysis of protein sequences identified 10 conserved motifs, with motif 1 potentially representing the GST domain. Analysis of cis-acting elements in the StGSTs promoter regions suggested their involvement in stress response pathways. RNA-seq analysis revealed that most StGSTs responded to both drought stress and DNA demethylation treatments. Quantitative PCR validation of 16 selected StGSTs identified four members that showed strong responses to both treatments, with distinct expression patterns between drought-tolerant (QS9) and drought-sensitive (ATL) varieties. Transient expression assays in tobacco demonstrated that these four StGSTs enhanced drought tolerance and may be regulated through DNA methylation pathways, though the precise mechanisms require further investigation. These findings provide a theoretical foundation for understanding the response and epigenetic regulation of potato GST genes under drought stress.