Bovine mastitis is a major bioeconomic and animal health challenge in dairy systems and is traditionally managed with intensive antibiotic therapy, contributing to antimicrobial resistance (AMR). This study explored the therapeutic potential of essential oils (EOs) from two native species of the Valdivian temperate rainforest, Laureliopsis philippiana (Tepa; LP_EO) and Drimys winteri (Canelo; DW_EO), against priority mastitis pathogens. Gas Chromatography–Mass Spectrometry (GC–MS) was used to characterize EO composition, and in vitro antibacterial and antifungal activities were evaluated against clinical isolates of Staphylococcus aureus, Streptococcus uberis and the azole-resistant yeast Pichia kudriavzevii by disk diffusion and broth microdilution assays. Both EOs were dominated by monoterpenes; LP_EO was richer in oxygenated monoterpenes (eucalyptol, terpinen-4-ol), whereas DW_EO showed a pinene-rich profile (β-pinene, α-pinene). DW_EO produced significantly larger inhibition zones than LP_EO against S. aureus and P. kudriavzevii and exhibited lower MIC₅₀/MIC₉₀ values for S. aureus, S. uberis and P. kudriavzevii. Notably, DW_EO showed a higher inhibitory activity against P. kudriavzevii with a MIC₉₀ of 4 mg/mL. These findings support DW_EO as a high-potential dual-action phytotherapeutic candidate for developing formulations and complementary tools within sustainable bovine udder health and antimicrobial stewardship frameworks.