The novel coronavirus disease (COVID-19) has resulted in a global pandemic. Recently, COVID-19-related pneumothorax has gained attention because of the associated prolonged hospital stay and high mortality. While most cases of pneumothorax respond well to conservative and supportive care, some cases of refractory pneumothorax with persistent air leaks (PALs) do not respond to conventional therapies. There is a lack of evidence-based management strategies to this regard. We describe the case of a 73-year-old man with COVID-19-related acute respiratory distress syndrome (ARDS) who developed delayed tension pneumothorax with PALs caused by alveolopleural fistulas. Despite chest tube drainage, autologous blood pleurodesis, and endoscopic procedures, the PALs could not be closed, and were complicated by thoracic empyema. Subsequent minimally invasive open-window thoracostomy (OWT) with vacuum-assisted closure (VAC) therapy helped successfully control the refractory PALs. Serial chest computed tomography monitoring was useful for the early detection of the pneumothorax and understanding of its temporal relationship with air-filled lung cysts. Our case provides a new perspective to the underlying cause of refractory pneumothorax with PALs, secondary to COVID-19-related ARDS, and underscores the potential of OWT with VAC therapy as a therapeutic alternative in such cases.