Nearly 1 year into the coronavirus disease 2019 pandemic, the first severe acute respiratory syndrome coronavirus 2 vaccines received emergency use authorisation and vaccination campaigns began. A number of factors can reduce the averted burden of cases and deaths due to vaccination. Here, we use a dynamic model, parametrised with Bayesian inference methods, to assess the effects of non-pharmaceutical interventions (NPIs) (such as social distancing, mask mandates, school and workplace closure), and vaccine administration and uptake rates on infections and deaths averted in the United States. We show that scenarios depicting higher compliance with NPIs avert more than 60% of infections and 70% of deaths during the period of vaccine administration, and that increasing the vaccination rate from 5 to 11 million people per week could increase the averted burden by more than one-third. These findings underscore the importance of maintaining NPIs and increasing vaccine administration rates.