The emergence of numerous variants of SARS-CoV-2, the causative agent of COVID-19, has presented new challenges to the global efforts to control the COVID-19 pandemic. Here, we obtain two cross-neutralizing antibodies (7D6 and 6D6) that target Sarbecoviruses' receptor-binding domain (RBD) with sub-picomolar affinities and potently neutralize authentic SARS-CoV-2. Crystal structures show that both antibodies bind a cryptic site different from that recognized by existing antibodies and highly conserved across Sarbecovirus isolates. Binding of these two antibodies to the RBD clashes with the adjacent N-terminal domain and disrupts the viral spike. Both antibodies confer good resistance to mutations in the currently circulating SARS-CoV-2 variants. Thus, our results have direct relevance to public health as options for passive antibody therapeutics and even active prophylactics. They can also inform the design of pan-sarbecovirus vaccines.