We report the universal boosting impact of a true negative capacitance (NC) effect on digital and analog performances of Tunnel FETs (TFETs), mirrored for the first time in near hysteresis-free experiments and exploiting the S-shaped polarization characteristics. Well behaved InGaAs TFETs with a minimum swing of 55 mV/dec at room temperature are combined with high-quality single crystalline PZT capacitors, placed in series with the gate. When fully satisfying the exact NC matching conditions by a single crystalline ferroelectric that can perform a mono-domain state, a hysteresis-free (sub-10 mV over 4 decades of current) NC-TFET with a sub-thermionic swing and an SS. of 40 mV/dec is demonstrated. In other devices, improvement in the subthreshold swing, down to 30 mV/dec, and analog current efficiency factor, up to 180 V-1, are achieved in NC-TFETs with a hysteresis as small as 30 mV. Importantly, the I-60 FoM of the TFET is improved up to 2 orders of magnitude. The supply voltage is thereby reduced by 50%, down to 300 mV, providing the same drive current. Our results show that NC can open a new direction as a universal performance booster in the FET design by significantly improving the low I-60 and low overdrive of TFETs.