Medicinal plants with multiple targets of action have become one of the most promising solutions in the fight against multidrug-resistant (MDR) bacterial infections. Tanacetum vulgare (Tansy) is one of the medicinal plants with antibacterial qualities that deserve to be studied. Thus, this research takes a closer look at tansy extract's composition and antibacterial properties, aiming to highlight its potential against clinically relevant bacterial strains. In this respect, the antibacterial test was performed against several drug-resistant pathogenic strains, and we correlated them with the main isolated compounds, demonstrating the therapeutic properties of the extract. The essential oil was extracted via hydrodistillation, and its composition was characterized via gas chromatography. The main isolated compounds known for their antibacterial effects were α-Thujone, β-Thujone, Eucalyptol, Sabinene, Chrysanthenon, Camphor, Linalool oxide acetate, cis-Carveol, trans-Carveyl acetate, and Germacrene. The evaluation of the antibacterial activity was carried out using the Kirby-Bauer and binary microdilution methods on Gram-positive and Gram-negative MDR strains belonging to the ESKAPE group (i.e., Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa, and Enterobacter spp.). Tansy essential oil showed MIC values ranging from 62.5 to 500 μg/mL against the tested strains. Synergistic activity with different classes of antibiotics (penicillins, cephalosporins, carbapenems, monobactams, aminoglycosides, and quinolones) has also been noted. The obtained results demonstrate that tansy essential oil represents a promising lead for developing new antimicrobials active against MDR alone or in combination with antibiotics.