The electrical resistivity ρ and magnetization M of α-R2S3 (R = Sm, Dy) single crystals have been measured in various magnetic fields lying in the ac-plane of an orthorhombic crystal structure. The measurements have been carried out by rotating the single crystals around the b-axis (being set parallel to a horizontal direction), corresponding to the longitudinal direction of needle-shaped single crystals, in vertical magnetic fields. The electrical resistivity under no magnetic field shows huge enhancement in a narrow temperature range around the successive magnetic transition temperatures, as reported previously. Such enhancement is suppressed rapidly by applying a magnetic field, which has been clearly seen as diminishing of the ρ(T) peak. The magnetic field along the easy magnetization axis; Heasy, moves the ρ(T) peak toward higher temperature with diminishing it, while the magnetic field along the hard magnetization axis; Hhard, moves it to lower temperature. The suppression effect is extremely anisotropic for the orientation of the magnetic field lying in the ac-plane. It has been concluded that Heasy suppresses the ρ enhancement most strongly. The suppression effect under Heasy is more than 200 times larger at least in some cases than that under Hhard.