We investigate manifestations of topological order in monoaxial helimagnet Cr1/3NbS2 by performing transport measurements on ultrathin crystals. Upon sweeping the magnetic field perpendicularly to the helical axis, crystals thicker than one helix pitch (48 nm) but much thinner than the magnetic domain size (∼1  μm) are found to exhibit sharp and hysteretic resistance jumps. We show that these phenomena originate from transitions between topological sectors with a different number of magnetic solitons. This is confirmed by measurements on crystals thinner than 48 nm—in which the topological sector cannot change—that do not exhibit any jump or hysteresis. Our results show the ability to deterministically control the topological sector of finite-size Cr1/3NbS2 and to detect intersector transitions by transport measurements.