Final answer:
Fentanyl is the analgesic drug that depresses the central nervous system.
Step-by-step explanation:
The analgesic drug that depresses the central nervous system is Fentanyl. Fentanyl is a powerful opioid that is typically used for severe pain relief, such as during surgery or for cancer patients. It acts on the central nervous system to reduce pain and can also cause drowsiness and respiratory depression.