BACKGROUND: Vaccination was the single most effective measure in mitigating the impact of the COVID-19 pandemic. Our study aims to quantify the impact of vaccination programmes during the initial year of vaccination (2021) by estimating the number of case fatalities avoided, using Sweden as a case study. METHODS: Using Swedish data on age-specific reported incidence and vaccination uptake, along with vaccine efficacies, age-specific contact patterns and under-reporting from the literature, we fit a Bayesian SEIR epidemic model with time-varying community contact rate for COVID-19 incidence. Age-specific fatality rates from the literature are adjusted proportionally to fit the observed number of case fatalities in the factual analysis, resulting in 5,510 (95% PI: 5,370-5,650) matching the observed number 5,430. The estimated time-varying community contact rate is then used in a counterfactual analysis where the population is unvaccinated, leading to more infections and fatalities. A sensitivity analysis is performed to identify which parameters influence our conclusions. FINDINGS: The counterfactual analysis result in a severe epidemic outbreak during the early autumn of 2021, resulting in about 37,100 (36,700-37,500) number of case fatalities. Consequently, the number of lives saved by the vaccination programme is estimated to be about 31,600 (31,300-32,000), out of which 5,170 are directly saved and 26,400 are indirectly saved, mainly by drastically reducing the severe outbreak in the early autumn of 2021, which would have occurred without vaccination and unchanged community contact rate. INTERPRETATION: Our mathematical model is used to analyse the impact of COVID-19 vaccination on lives saved in Sweden during 2021, but the same methodology can be applied to other countries. The counterfactual analysis offers insights into an alternative trajectory of the pandemic without vaccination. The results show the direct impact of vaccination on reducing deaths for infected individuals and shed light on the indirect effects of reduced transmission dynamics.