We report on an ultrafast photoinduced phase transition with a strikingly long-lived Martensitic anomaly driven by above-threshold single-cycle terahertz (THz) pulses in Nb$_3$Sn. A non-thermal, THz-induced depletion of low frequency conductivity indicates increased gap splitting of high energy $Gamma_{12}$ bands by removal of their degeneracies which enhances the Martensitic phase. In contrast, optical pumping leads to a $Gamma_{12}$ gap melting. Such light-induced non-equilibrium Martensitic instability persists up to a critical temperature $sim$100 K, i.e., more than twice the equilibrium temperature, and can be stabilized beyond technologically-relevant, nanosecond timescales. Together with first-principle simulations, we identify a compelling THz tuning of structural fluctuations via E$_u$ phonons to achieve a non-equilibrium ordering at high temperatures far exceeding those for equilibrium states.