The search for synergies between natural products and commercial antibiotics is a promising strategy against bacterial resistance. This study determined the antimicrobial capacity of Nerol (NE) and Tannic Acid (TA) against 14 pathogenic bacteria, including ESKAPE pathogens. TA exhibited the lowest Minimum Inhibitory Concentrations (MICs) at 162.5 µg/mL against Pasteurella aerogenes and 187.5 µg/mL against Acinetobacter baumannii (WHO priority 1). NE showed its lowest MIC of 500 µg/mL against both Pasteurella aerogenes and Salmonella enterica. A total of 35 combinations of NE and 13 of TA with eight commercial antibiotics were analyzed. For NE, combinations with Streptomycin and Gentamicin were effective against Salmonella enterica, Bacillus subtilis, and Streptococcus agalactiae, with antibiotic MIC reductions between 75.0 and 87.5%. TA showed six synergies with Chloramphenicol, Ampicillin, Erythromycin, and Streptomycin against Acinetobacter baumannii, Streptococcus agalactiae, and Pasteurella aerogenes, with MIC reductions between 75.0 and 93.7%. Additionally, 31 additive effects with antibiotics for NE and 8 for TA were found. Kinetic studies on these synergies showed complete inhibition of bacterial growth, suggesting that natural products enhance antibiotics by facilitating their access to targets or preventing resistance. Given their safety profiles recognized by the EPA and FDA, these natural products could be promising candidates as antibiotic enhancers.