Context. Current exoplanet surveys using the radial velocity (RV) technique are targeting M dwarfs because any habitable zone terrestrial-mass planets will induce a high RV and orbit on shorter periods than for more massive stars. One of the main caveats is that M dwarfs show a wide range of activity levels from inactive to very active, which can induce an asymmetry in the line profiles and, consequently, a spurious RV measurement. Aims. We aim to benchmark the impact of stellar activity on high-precision RV measurements using regular-cadence CARMENES visible and near-infrared observations of the active M3.5 dwarf EV Lac. Methods. We used the newly developed technique of low-resolution Doppler imaging to determine the centre-of-light, or spot-induced RV component, for eight observational epochs. Results. We confirm a statistically significant and strong correlation between the independently measured centre-of-light and the chromatic index, which is a measure of the amplitude variation with wavelength of the RVs. We also find circular “closed-loop” relations of several activity indices with RV for a subset of data that covers only several rotation periods. We also investigate the implications of large phase gaps in the periodograms of activity indicators. Finally, by removing the spot-induced RV component we improve the planet-mass sensitivity by a factor of at least three. Conclusions. We conclude that for active M stars, a regular-cadence observing strategy is the most efficient way to identify and eliminate sources of correlated noise.