T Pyx is a luminous recurrent nova that accretes at a much higher rate than is expected for its photometrically determined orbital period of about 1.8 h. We here provide the first spectroscopic confirmation of the orbital period, P = 1.8295 h (f = 13.118368 ± 1.1 × 10 −5 c d −1 ), based on time-resolved optical spectroscopy obtained at the Very Large Telescope and the Magellan telescope. We also derive an upper limit of the velocity semi-amplitude of the white dwarf, K1 = 17.9 ± 1.6 km s −1 , and estimate a mass ratio of q = 0.20 ± 0.03. If the mass of the donor star is estimated using the period-density relation and theoretical main-sequence mass-radius relation for a slightly inflated donor star, we find M 2 = 0.14 ± 0.03 M . This implies a mass of the primary white dwarf of M 1 = 0.7 ± 0.2 M . If the white-dwarf mass is >1 M , as classical nova models imply, the donor mass must be even higher. We therefore rule out the possibility that T Pyx has evolved beyond the period minimum for cataclysmic variables. We find that the system inclination is constrained to be i ≈ 10 • , confirming the expectation that T Pyx is a low-inclination system. We also discuss some of the evolutionary implications of the emerging physical picture of T Pyx. In particular, we show that epochs of enhanced mass transfer (like the present) may accelerate or even dominate the overall evolution of the system, even if they are relatively short-lived. We also point out that such phases may be relevant to the evolution of cataclysmic variables more generally.