Trisomy 21, or Down syndrome (DS), is neonates' most common chromosomal abnormality. In addition, children born with DS have an increased risk of congenital anomalies such as congenital heart defects, gastrointestinal abnormalities, and, rarely, cleft palate. Cleft lip and palate are among the most common congenital anomalies associated with many congenital syndromes; however, Trisomy 21 is the least common congenital anomaly associated with orofacial clefts. We present a case of cleft palate, duodenal stenosis, persistent pulmonary hypertension of the newborn, patent ductus arteriosus, and atrial septal defect in a newborn with classical clinical features of Down syndrome. This report discusses the uncommon presentation of trisomy 21 and concomitant cleft palate in a neonate, including its recognition and treatment, as no standard of care treatment exists.