Bacterial spot of stone fruits caused by Xanthomonas arboricola pv. pruni (Xap) is one of the most significant diseases of several Prunus species. Disease outbreaks can result in severe economic losses while the control options are limited. Antibacterial efficacy of essential oils (EOs) of thyme, cinnamon, clove, rosemary, tea tree, eucalyptus, lemon grass, citronella grass, and lemon balm was assessed against two Hungarian Xap isolates. The minimal inhibitory concentration (MIC) was determined by broth microdilution assay and for the identification of active EOs’ components a newly introduced high-performance thin-layer chromatography (HPTLC)-Xap (direct bioautography) method combined with solid-phase microextraction-gas chromatography/mass spectrometry (SPME-GC/MS) was applied. All EOs inhibited both bacterium isolates, but cinnamon proved to be the most effective EO with MIC values of 31.25 µg/mL and 62.5 µg/mL, respectively. Compounds in the antibacterial HPTLC zones were identified as thymol in thyme, trans-cinnamaldehyde in cinnamon, eugenol in clove, borneol in rosemary, terpinen-4-ol in tea tree, citral (neral and geranial) in lemon grass and lemon balm, and citronellal and nerol in citronella grass. Regarding active compounds, thymol had the highest efficiency with a MIC value of 50 µg/mL. Antibacterial effects of EOs have already been proven for several Xanthomonas species, but to our knowledge, the studied EOs, except for lemon grass and eucalyptus, were tested for the first time against Xap. Furthermore, in case of Xap, this is the first report demonstrating that direct bioautography is a fast and suitable method for screening anti-Xap components of complex matrices, like EOs.