Essential oils (EOs) are complex mixtures of terpenic and phenolic volatiles, although other groups of compounds can be present in high proportions. Due to their strong biological activities, EOs have been increasingly screened for nematicidal activity against plant parasitic nematodes of crops and forest species. Direct-contact bioassays can provide important data on the properties of anti-nematodal chemical structures. In previous studies, the EO of Satureja montana, winter savory, revealed a high nematicidal activity against the pinewood nematode (PWN), a dangerous phytoparasite that attacks pine trees and causes pine wilt disease in susceptible trees. The bioactivity of S. montana EO was attributed to its oxygen-containing molecules, while the hydrocarbon molecules showed only a weak activity. However, the interactions between EO compounds was not ascertained. In the present study, the main compounds of winter savory EO, i.e., the phenol carvacrol (64%), and the hydrocarbons γ-terpinene (18%) and p-cymene (8%) were tested solely to pinpoint the main responsible for the nematicidal strength of the EO; and in binary combinations to assess synergistic or antagonistic interactions. Direct-contact bioassays were performed for the compounds and their binary combinations at the proportions they presented in the original EO. Carvacrol, induced the strongest response, inducing complete PWN mortality at a concentration as low as 0.5 mg/mL, however, γ-terpinene and p-cymene appear to influence its activity, even though they induced a low PWN mortality at 1 mg/mL. Uncovering the interactions between the components of nematicidal EOs can provide clues to formulate more effective sustainable alternatives to traditional pesticides.