Across biological scales, gene-regulatory networks employ autorepression (negative feedback) to maintain homeostasis and minimize failure from aberrant expression. Here, we present a proof of concept that disrupting transcriptional negative feedback dysregulates viral gene expression to therapeutically inhibit replication and confers a high evolutionary barrier to resistance. We find that nucleic-acid decoys mimicking cis-regulatory sites act as "feedback disruptors," break homeostasis, and increase viral transcription factors to cytotoxic levels (termed "open-loop lethality"). Feedback disruptors against herpesviruses reduced viral replication >2-logs without activating innate immunity, showed sub-nM IC₅₀, synergized with standard-of-care antivirals, and inhibited virus replication in mice. In contrast to approved antivirals where resistance rapidly emerged, no feedback-disruptor escape mutants evolved in long-term cultures. For SARS-CoV-2, disruption of a putative feedback circuit also generated open-loop lethality, reducing viral titers by >1-log. These results demonstrate that generating open-loop lethality, via negative-feedback disruption, may yield a class of antimicrobials with a high genetic barrier to resistance.