The Mars hemispheric dichotomy is expressed as a dramatic difference in elevation, crustal thickness and crater density between the southern highlands and northern lowlands (which cover ~42% of the surface). Despite the prominence of the dichotomy, its origin has remained enigmatic and models for its formation largely untested. Endogenic degree-1 convection models with north-south asymmetry are incomplete in that they are restricted to simulating only mantle dynamics and they neglect crustal evolution, whereas exogenic multiple impact events are statistically unlikely to concentrate in one hemisphere. A single mega-impact of the requisite size has not previously been modelled. However, it has been hypothesized that such an event could obliterate the evidence of its occurrence by completely covering the surface with melt or catastrophically disrupting the planet. Here we present a set of single-impact initial conditions by which a large impactor can produce features consistent with the observed dichotomy's crustal structure and persistence. Using three-dimensional hydrodynamic simulations, large variations are predicted in post-impact states depending on impact energy, velocity and, importantly, impact angle, with trends more pronounced or unseen in commonly studied smaller impacts. For impact energies of ~(3-6)×1029J, at low impact velocities (6-10kms-1) and oblique impact angles (30-60°), the resulting crustal removal boundary is similar in size and ellipticity to the observed characteristics of the lowlands basin. Under these conditions, the melt distribution is largely contained within the area of impact and thus does not erase the evidence of the impact's occurrence. The antiquity of the dichotomy is consistent with the contemporaneous presence of impactors of diameter 1,600-2,700km in Mars-crossing orbits, and the impact angle is consistent with the expected distribution.