Objective: to verify the frequency of congenital infections in newborns and their possible associations with the universal-neonatal-hearing-screening (UNHS) results, and evaluate a reference UNHS service in the Unified Health System (Sistema Único de Saúde—SUS), according to quality indicators. Methods: Historical cohort study with data analysis of newborns attending prestigious hearing-health SUS services from January 2017 to December 2021, in Santa Catarina, Brazil. The quality of screening coverage was assessed based on the quality indicators proposed by the Brazilian neonatal-hearing-screening-care guidelines (Diretrizes de Atenção da Triagem Auditiva Neonatal—DATAN). Logistic-regression analysis, crude OR calculations, Cochran–Mantel–Haenszel OR calculation, and chi-square test were performed to estimate the association between risk indicators for hearing loss and UNHS failure. Results: In the last five years, the prestigious services performed UNHS on 34,801 newborns and met the DATAN quality indicators. Congenital syphilis was the most frequent (1.59%) congenital infection in newborns, followed by HIV (0.87%), whereas the least frequent was rubella (0.029%). Conclusion: Prestigious UNHS services reached ≥95% hearing screening coverage. Considering all congenital infections, the prevalence was 2.87%, with congenital syphilis the most frequent. Newborns with congenital syphilis or HIV are more likely to fail UNHS.