Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo₂V₂O₈ in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.