The risk of zoonotic coronavirus spillover into the human population, as highlighted by the SARS-CoV-2 pandemic, demands the development of pan-coronavirus antivirals. The efficacy of existing antiviral ribonucleoside/ribonucleotide analogs, such as remdesivir, is decreased by the viral proofreading exonuclease NSP14-NSP10 complex. Here, using a novel assay and in silico modeling and screening, we identified NSP14-NSP10 inhibitors that increase remdesivir's potency. A model compound, sofalcone, both inhibits the exonuclease activity of SARS-CoV-2, SARS-CoV, and MERS-CoV in vitro, and synergistically enhances the antiviral effect of remdesivir, suppressing the replication of SARS-CoV-2 and the related human coronavirus OC43. The validation of top hits from our primary screenings using cellular systems provides proof-of-concept for the NSP14 complex as a therapeutic target.