Staphylococcus aureus frequently causes subclinical mastitis around the world with a high impact on the milk industry and public health. Essential oils (EO) are recognized antimicrobials that can be synergistic with antibiotics. The main objective of this study was to evaluate the essential oil (EO) of Melaleuca armillaris as an adjuvant of erythromycin (ERY) for the alternative treatment of bovine mastitis caused by S. aureus. The Minimum Inhibitory and Bactericidal Concentrations (MIC and MBC) of EO, ERY, and its combinations were established against S. aureus at different pHs (7.4, 6.5 and 5.0), emulating extra and intracellular conditions. Sensitive (N = 3) and resistant (N = 3) strains to ERY and S. aureus ATCC 29213 as control were used. Math models were applied to describe the antibacterial activity of EO and combinations EO-ERY. The EO was bactericidal against all the strains independently of the pH with a slight improvement in acid conditions. The synergism between EO and ERY was estimated by the Fractional Inhibitory Concentration Index (FIC) and by mathematical modeling of the bacterial killing data. Synergism was observed with ERY, where combinations had bactericidal activity also even with pH modification. M. armillaris EO is an interesting adjuvant for ERY, being a promissory option for further analysis of intracellular efficacy against S. aureus.