Neutralizing antibodies (NAbs) can prevent and treat infections caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). However, continuously emerging variants, such as Omicron, have significantly reduced the potency of most known NAbs. The selection of NAbs with broad neutralizing activities and the identification of conserved critical epitopes are still urgently needed. Here, we identified an extremely potent antibody (55A8) by single B-cell sorting from convalescent SARS-CoV-2-infected patients that recognized the receptor-binding domain (RBD) in the SARS-CoV-2 spike (S) protein. 55A8 could bind to wild-type SARS-CoV-2, Omicron BA.1 and Omicron BA.2 simultaneously with 58G6, a NAb previously identified by our group. Importantly, an antibody cocktail containing 55A8 and 58G6 (2-cocktail) showed synergetic neutralizing activity with a half-maximal inhibitory concentration (IC50) in the picomolar range in vitro and prophylactic efficacy in hamsters challenged with Omicron (BA.1) through intranasal delivery at an extraordinarily low dosage (25 μg of each antibody daily) at 3 days post-infection. Structural analysis by cryo-electron microscopy (cryo-EM) revealed that 55A8 is a Class III NAb that recognizes a highly conserved epitope. It could block angiotensin-converting enzyme 2 (ACE2) binding to the RBD in the S protein trimer via steric hindrance. The epitopes in the RBD recognized by 55A8 and 58G6 were found to be different and complementary, which could explain the synergetic mechanism of these two NAbs. Our findings not only provide a potential antibody cocktail for clinical use against infection with current SARS-CoV-2 strains and future variants but also identify critical epitope information for the development of better antiviral agents.