  We investigate the time evolution towards the asymptotic steady state of a
one dimensional interacting system after a quantum quench. We show that at
finite time the latter induces entanglement between right- and left- moving
density excitations, encoded in their cross-correlators, which vanishes in the
long-time limit. This behavior results in a universal time-decay in system
spectral properties $ \propto t^{-2} $, in addition to non-universal power-law
contributions typical of Luttinger liquids. Importantly, we argue that the
presence of quench-induced entanglement clearly emerges in transport
properties, such as charge and energy currents injected in the system from a
biased probe, and determines their long-time dynamics. In particular, energy
fractionalization phenomenon turns out to be a promising platform to observe
the universal power-law decay $ \propto t^{-2} $ induced by entanglement and
represents a novel way to study the corresponding relaxation mechanism.
