Nanowire tunnel field-effect transistors (TFETs) have been proposed as the most advanced one-dimensional (1D) devices that break the thermionic 60 mV/decade of the subthreshold swing (SS) of metal oxide semiconductor field-effect transistors (MOSFETs) by using quantum mechanical band-to-band tunneling and excellent electrostatic control. Meanwhile, negative capacitance (NC) of ferroelectrics has been proposed as a promising performance booster of MOSFETs to bypass the aforementioned fundamental limit by exploiting the differential amplification of the gate voltage under certain conditions. We combine these two principles into a single structure, a negative capacitance heterostructure TFET, and experimentally demonstrate a double beneficial effect: (i) a super-steep SS value down to 10 mV/decade and an extended low slope region that is due to the NC effect and, (ii) a remarkable off-current reduction that is experimentally observed and explained for the first time by the effect of the ferroelectric dipoles, which set the surface potential in a slightly negative value and further blocks the source tunneling current in the off-state. State-of-the-art InAs/InGaAsSb/GaSb nanowire TFETs are employed as the baseline transistor and PZT and silicon-doped HfO2 as ferroelectric materials.