We investigated the financial performance of a sample of sustainable investment funds in terms of returns, volatility, and contagion risk during the financial crisis caused by the COVID-19 pandemic. In order to conduct a more reliable analysis, we considered a homogenous sample composed of 30 funds declaring the same benchmark (the MSCI Europe index). The Morningstar Sustainability ESG rating was used to determine the level of sustainability of each fund. Both the GARCH models and the event study suggest that funds with a higher ESG rating were able to outperform other funds during the COVID-19 period. These funds had a greater level of resilience and exhibited a lower level of risk contagion during the pandemic. These instruments appear to assume the role of risk protection and should be considered a means of both promoting sustainable growth and minimizing portfolio risk.