Methicillin-resistant Staphylococcus aureus (MRSA) is a notorious pathogen responsible for not only a number of difficult-to-treat hospital-acquired infections, but also for infections that are community- or livestock-acquired. The increasing lack of efficient antibiotics has renewed the interest in lytic bacteriophages (briefly phages) as additional antimicrobials against multi-drug resistant bacteria, including MRSA. The aim of this study was to test the hypothesis that a combination of the well-known and strictly lytic S. aureus phage Sb-1 and oxacillin, which as sole agent is ineffective against MRSA, exerts a significantly stronger bacterial reduction than either antimicrobial alone. Eighteen different MRSA isolates and, for comparison, five MSSA and four reference strains were included in this study. The bacteria were challenged with a combination of varying dosages of the phage and the antibiotic in liquid medium using five different antibiotic levels and four different viral titers (i.e., multiplicity of infections (MOIs) ranging from 10−5 to 10). The dynamics of the cell density changes were determined via time-kill assays over 16 h. Positive interactions between both antimicrobials in the form of facilitation, additive effects, or synergism were observed for most S. aureus isolates. These enhanced antibacterial effects were robust with phage MOIs of 10−1 and 10 irrespective of the antibiotic concentrations, ranging from 5 to 100 µg/mL. Neutral effects between both antimicrobials were seen only with few isolates. Importantly, antagonism was a rare exception. As a conclusion, phage Sb-1 and oxacillin constitute a robust heterologous antimicrobial pair which extends the efficacy of a phage-only approach for controlling MRSA.