COVID-19 vaccination in Brazil required a phased program, with priorities for age groups, health workers, and vulnerable people. Social distancing and isolation interventions have been essential to mitigate the advance of the pandemic in several countries. We developed a mathematical model capable of capturing the dynamics of the SARS-CoV-2 dissemination aligned with social distancing, isolation measures, and vaccination. Surveillance data from the city of Rio de Janeiro provided a case study to analyze possible scenarios, including non-pharmaceutical interventions and vaccination in the epidemic scenario. Our results demonstrate that the combination of vaccination and policies of transmission suppression potentially lowered the number of hospitalized cases by 380+ and 66+ thousand cases, respectively, compared to an absence of such policies. On top of transmission suppression-only policies, vaccination impacted more than 230+ thousand averted hospitalized cases and 43+ thousand averted deaths. Therefore, health surveillance activities should be maintained along with vaccination planning in scheduled groups until a large vaccinated coverage is reached. Furthermore, this analytical framework enables evaluation of such scenarios.