The vaccines developed in 2020-2021 against the SARS-CoV-2 virus were designed to prevent severity and deaths due to COVID-19. However, how effective this vaccination campaign was at saving lives remains a methodological challenge. In this work, we developed a Bayesian statistical model to estimate the number of deaths and hospitalizations in individuals above 60 years old in Brazil. Using the actual number of hospitalized and deaths from the Brazilian database, and also the coverage of second dose according to the National Immunization Program, we rebuilt the realized scenario as well as the hypothetical scenario without vaccination in Brazil in order to perform a counterfactual analysis. By computing the difference between the hypothetical and realized scenarios, we were able to estimate the direct effect of COVID-19 vaccination in Brazil. We also evaluated two other hypothetical, but not impossible, scenarios considering earlier vaccination roll-outs. We estimated that more than 165 thousand of 60+ years old individuals were not hospitalized due to COVID-19 until August 28, 2021, and other approximately 100 thousand individuals could not have been hospitalized if the immunization started as soon it was approved in Brazil. We also estimate that more than 75 thousand lives were saved in the period analysed for the same age group, and additional 48 thousand lives could have been saved if the Brazilian Government started the immunization 8 weeks earlier.