Sleep-disordered breathing (SDB) is highly prevalent in patients with heart failure (HF), and is known to be associated with a worse prognosis. The severity of central sleep apnea is thought to mirror cardiac dysfunction. The novel angiotensin receptor-neprilysin inhibitor (ARNi) sacubitril has been shown to improve HF, but a relationship between treatment with ARNi and the severity of SDB has not yet been investigated. We report the case of a 71-year-old male with HF and SDB. Treatment with sacubitril/valsartan was associated with improved cardiac function, as shown by a reduction in the level of N-terminal prohormone of brain natriuretic peptide from 3,249 to 1,720 pg/mL, and an improvement in left-ventricular ejection fraction from 30 to 35%. This was accompanied by a marked reduction in the apnea-hypopnea index (from 41 to 19/h). To the best of our knowledge, this is the first case to document parallel improvements in HF and SDB after the initiation of ARNi treatment.