Viral-deletion mutants that conditionally replicate and inhibit the wild-type virus (i.e., defective interfering particles, DIPs) have long been proposed as single-administration interventions with high genetic barriers to resistance. However, theories predict that robust, therapeutic DIPs (i.e., therapeutic interfering particles, TIPs) must conditionally spread between cells with R₀ >1. Here, we report engineering of TIPs that conditionally replicate with SARS-CoV-2, exhibit R₀ >1, and inhibit viral replication 10- to 100-fold. Inhibition occurs via competition for viral replication machinery, and a single administration of TIP RNA inhibits SARS-CoV-2 sustainably in continuous cultures. Strikingly, TIPs maintain efficacy against neutralization-resistant variants (e.g., B.1.351). In hamsters, both prophylactic and therapeutic intranasal administration of lipid-nanoparticle TIPs durably suppressed SARS-CoV-2 by 100-fold in the lungs, reduced pro-inflammatory cytokine expression, and prevented severe pulmonary edema. These data provide proof of concept for a class of single-administration antivirals that may circumvent current requirements to continually update medical countermeasures against new variants.