By making use of a class of steep exponential type of potentials, which has been recently used to describe quintessential inflation, we show how a unified picture for both inflation, dark energy and dark matter can emerge entirely through dissipative effects. Dissipation provides a way for extending the applicability of a larger class of these potentials in the sense of leading to a consistent early Universe inflationary picture and producing observables in agreement with the Planck legacy data. Likewise, dissipative effects lead to dark matter production with consistent abundances and, towards the recent time of the Universe, drives the potential energy of the scalar quintessential field to dominate again, essentially mimicking a cosmological constant by today, with all cosmological parameters consistent with the observations. Both early and late Universes are connected and with no kination period in between.