Influenza viruses annually kill 290,000-650,000 people worldwide. Antivirals can reduce death tolls. Baloxavir, the recently approved influenza antiviral, inhibits initiation of viral mRNA synthesis, whereas oseltamivir, an older drug, inhibits release of virus progeny. Baloxavir blocks virus replication more rapidly and completely than oseltamivir, reducing the duration of infectiousness. Hence, early baloxavir treatment may indirectly prevent transmission. Here, we estimate impacts of ramping up and accelerating baloxavir treatment on population-level incidence using a new model that links viral load dynamics from clinical trial data to between-host transmission. We estimate that ~22 million infections and >6,000 deaths would have been averted in the 2017-2018 epidemic season by administering baloxavir to 30% of infected cases within 48 h after symptom onset. Treatment within 24 h would almost double the impact. Consequently, scaling up early baloxavir treatment would substantially reduce influenza morbidity and mortality every year. The development of antivirals against the SARS-CoV2 virus that function like baloxavir might similarly curtail transmission and save lives.