Initial replication of SARS-CoV-2 in the upper respiratory tract is required to establish infection, and the replication level correlates with the likelihood of viral transmission. Here, we examined the role of host innate immune defenses in restricting early SARS-CoV-2 infection using transcriptomics and biomarker-based tracking in serial patient nasopharyngeal samples and experiments with airway epithelial organoids. SARS-CoV-2 initially replicated exponentially, with a doubling time of ∼6 h, and induced interferon-stimulated genes (ISGs) in the upper respiratory tract, which rose with viral replication and peaked just as viral load began to decline. Rhinovirus infection before SARS-CoV-2 exposure accelerated ISG responses and prevented SARS-CoV-2 replication. Conversely, blocking ISG induction during SARS-CoV-2 infection enhanced viral replication from a low infectious dose. These results show that the activity of ISG-mediated defenses at the time of SARS-CoV-2 exposure impacts infection progression and that the heterologous antiviral response induced by a different virus can protect against SARS-CoV-2.