The current coronavirus disease 2019 (COVID-19) pandemic has impacted dense urban populations particularly hard. Here, we provide an in-depth characterization of disease incidence and mortality patterns, and their dependence on demographic and socioeconomic strata in Santiago, a highly segregated city and the capital of Chile. We find that among all age groups, there is a strong association between socioeconomic status and both mortality -measured either by direct COVID-19 attributed deaths or excess deaths- and public health capacity. Specifically, we show that behavioral factors like human mobility, as well as health system factors such as testing volumes, testing delays, and test positivity rates are associated with disease outcomes. These robust patterns suggest multiple possibly interacting pathways that can explain the observed disease burden and mortality differentials: (i) in lower socioeconomic status municipalities, human mobility was not reduced as much as in more affluent municipalities; (ii) testing volumes in these locations were insufficient early in the pandemic and public health interventions were applied too late to be effective; (iii) test positivity and testing delays were much higher in less affluent municipalities, indicating an impaired capacity of the health-care system to contain the spread of the epidemic; and (iv) infection fatality rates appear much higher in the lower end of the socioeconomic spectrum. Together, these findings highlight the exacerbated consequences of health-care inequalities in a large city of the developing world, and provide practical methodological approaches useful for characterizing COVID-19 burden and mortality in other segregated urban centers.