Staphylococcus aureus is the major subclinical mastitis-causing pathogen in dairy cows. In some European and Latin American countries, rifaximin (RIF) is a commonly used therapy at drying off. Phytotherapeutics are alternatives for the treatment of infectious diseases. Melaleuca armillaris essential oil (EO) has been reported as a good antimicrobial against S. aureus. The aim of this work was to investigate, in vitro, the combined effect of EO and RIF to identify a synergic interaction against S. aureus in order to obtain enough information for subsequent pharmacokinetic/pharmacodynamic studies. The minimum inhibitory concentrations (MIC) for RIF, EO, and combinations of these against S. aureus strains were determined at pH 7.4, 6.5, and 5.0, representing intracellular conditions where S. aureus is usually located. The fractional inhibitory concentration index (FIC) and the index of antibacterial activity (E) were evaluated. The MIC of EO at pH 7.4 was 25–12.5 μL/mL and decreased with the acidity of the medium. RIF presented a high antimicrobial activity (0.032 μg/mL) against S. aureus regardless of the pH conditions. Combining RIF with EO, we found a synergic effect. A mix of 0.004 μg/mL of RIF and 12.5 μL/mL of EO led to a virtual eradication effect against wild-type strains at pH 7.4. Media acidification improves the EO/RIF activity, so EO would be a good adjuvant for RIF to treat staphylococcal infections and decrease antimicrobial resistance.