Aims: The chemical evolution of galaxies on a cosmological timescale is still a matter of debate despite the increasing number of available data provided by spectroscopic surveys of star-forming galaxies at different redshifts. The fundamental relations involving metallicity, such as the mass - metallicity relation (MZR) or the fundamental metallicity relation, give controversial results about the reality of evolution of the chemical content of galaxies at a given stellar mass. In this work we shed some light on this issue using the completeness reached by the 20 k bright sample of the zCOSMOS survey and using for the first time the nitrogen-to-oxygen ratio (N/O) as a tracer of the gas phase chemical evolution of galaxies that is independent of the star formation rate. Methods: Emission-line galaxies both in the SDSS and 20 k zCOSMOS bright survey were used to study the evolution from the local Universe of the MZR up to a redshift of ~1.32, and the relation between stellar mass and N/O (MNOR) up to a redshift of ~0.42 using the N2S2 parameter. All the physical properties derived from stellar continuum and gas emission-lines, including stellar mass, star formation rates, metallicity and N/O, were calculated in a self-consistent way over the full redshift range. Results: We confirm the trend to find lower metallicities in galaxies of a given stellar mass in a younger Universe. This trend is even observed when taking possible effects into account that are due to the observed larger median star formation rates for galaxies at higher redshifts. We also find a significant evolution of the MNOR up to z ~ 0.4. Taking the slope of the O/H vs. N/O relation into account for the secondary-nitrogen production regime, the observed evolution of the MNOR is consistent with the trends found for both the MZR and its equivalent relation using new expressions to reduce its dependence on star formation rate.