Hairy roots (HRs) grown in vitro are a powerful platform for plant biotechnological advances and for the bio-based production of metabolites of interest. In this work, black carrot HRs able to accumulate anthocyanin as major secondary metabolite were used. Biomass and anthocyanin accumulation were improved by modulating growth medium composition—different Murashige & Skoog (MS)-based media—and H2O2-elicitation, and the level of the main antioxidant enzymes on elicited HRs was measured. Higher growth was obtained on liquid 1/2 MS medium supplemented with 60 g/L sucrose for HRs grown over 20 days. In this medium, 200 µM H2O2 applied on day 12 induced anthocyanin accumulation by 20%. The activity of superoxide dismutase (SOD)—which generates H2O2 from O2•−—increased by over 50%, whereas the activity of H2O2-scavenging enzymes was not enhanced. Elicitation in the HRs can result in a controlled oxidative burst, in which SOD activity increased H2O2 levels, whereas anthocyanins, as effective reactive oxygen species scavengers, could be induced to modulate the oxidative burst generated. Moreover, given the proven stability of the HR lines used and their remarkable productivity, this system appears as suitable for elucidating the interplay between antioxidant and secondary metabolism.