The interruption of bacteriological surveillance due to the COVID-19 pandemic brought serious consequences, such as the collapse of health systems and the possible increase in antimicrobial resistance. Therefore, it is necessary to know the rate of resistance and its associated mechanisms in bacteria causing hospital infections during the pandemic. The aim of this work was to show the phenotypic and molecular characteristics of antimicrobial resistance in ESKAPE bacteria in a Mexican tertiary care hospital in the second and third years of the pandemic. For this purpose, during 2021 and 2022, two hundred unduplicated strains of the ESKAPE group (Escherichia coli, Klebsiella pneumoniae, Pseudomonas aeruginosa, and Acinetobacter baumannii) were collected from various clinical sources and categorized by resistance according to the CLSI. An analysis of variance (ANOVA) complemented by the Tukey test was performed to search for changes in antimicrobial susceptibility profiles during the study period. Finally, the mechanisms of resistance involved in carbapenem resistance were analyzed, and the search for efflux pumps and high-risk sequence types in A. baumannii was performed by multilocus analysis (MLST). The results showed no changes in K. pneumoniae resistance during the period analyzed. Decreases in quinolone resistance were identified in E. coli (p = 0.039) and P. aeruginosa (p = 0.03). Interestingly, A. baumannii showed increases in resistance to penicillins (p = 0.004), aminoglycosides (p < 0.001, p = 0.027), carbapenems (p = 0.027), and folate inhibitors (p = 0.001). Several genes involved in carbapenem resistance were identified (blaNDM, blaVIM, blaOXA, blaKPC, blaOXA-40, and blaOXA-48) with a predominance of blaOXA-40 and the adeABCRS efflux pump in A. baumannii. Finally, MLST analysis revealed the presence of globally distributed sequence types (ST369 and ST758) related to hospital outbreaks in other parts of the world. The results presented demonstrate that the ESKAPE group has played an important role during the COVID-19 pandemic as nosocomial antibiotic-resistant pathogens and in particular A. baumannii MDR as a potential reservoir of resistance genes. The implications of the increases in antimicrobial resistance in pathogens of the ESKAPE group and mainly in A. baumannii during the COVID-19 pandemic are analyzed and discussed.