Laurus nobilis L. (laurel, Lauraceae) and Prunus armeniaca L. (apricot, Rosaceae) are important industrial crops and display significant biological properties, including antimicrobial activity. In this work, essential oils (EOs) prepared from the leaves of both species from Morocco were evaluated for the first time for possible synergistic in vitro antibacterial and antifungal effects with some conventional antimicrobial drugs, namely fluconazole, ciprofloxacin and vancomycin. Samples were further evaluated for chemical composition by gas chromatography–mass spectrometry (GC-MS). The main volatile compounds detected in L. nobilis were eucalyptol (40.85%), α-terpinyl acetate (12.64%) and methyl eugenol (8.72%), while P. armeniaca was dominated essentially by (Z)-phytol (27.18%), pentacosane (15.11%), nonacosane (8.76%) and benzaldehyde (7.25%). Regarding antimicrobial activity, both EOs inhibited significantly all the microorganisms tested. The EO from L. nobilis had the highest activity, with minimal inhibitory concentrations (MICs) ranging from 1.39 to 22.2 mg/mL for bacteria and between 2.77 and 5.55 mg/mL for yeasts. Conversely, the combination of the studied EOs with ciprofloxacin, vancomycin and fluconazol resulted in a noteworthy decrease in their individual MICs. In fact, of the 32 interactions tested, 23 (71.87%) demonstrated total synergism and 9 (28.12%) a partial synergistic interaction. The EO from L. nobilis exhibited the highest synergistic effect with all the antibiotics used, with fractional inhibitory concentration (FIC) index values in the range of 0.266 to 0.75 for bacteria, and between 0.258 and 0.266 for yeast. The synergistic interaction between the studied EOs and standard antibiotics may constitute promising anti-infective agents useful for treating diseases induced by antibiotic-resistant pathogens.