Networks of interconnected inhibitory neurons, such as the thalamic reticular nucleus (TRN), often regulate neural oscillations. Thalamic circuits generate sleep spindles and may contribute to some forms of generalized absence epilepsy, yet the exact role of inhibitory connections within the TRN remains controversial. Here, by using mutant mice in which the thalamic effects of the anti-absence drug clonazepam (CZP) are restricted to either relay or reticular nuclei, we show that the enhancement of intra-TRN inhibition is both necessary and sufficient for CZP to suppress evoked oscillations in thalamic slices. Extracellular and intracellular recordings show that CZP specifically suppresses spikes that occur during bursts of synchronous firing, and this suppression grows over the course of an oscillation, ultimately shortening that oscillation. These results not only identify a particular anatomical and molecular target for anti-absence drug design, but also elucidate a specific dynamic mechanism by which inhibitory networks control neural oscillations.