Final answer:
Flumazenil should be administered immediately to reverse the effects of benzodiazepine-induced apnea and unresponsiveness by acting as a benzodiazepine antagonist at GABA-A receptors.
Step-by-step explanation:
In the event that a patient becomes apneic and unresponsive following the intravenous (IV) administration of a benzodiazepine, the drug that should be administered immediately is flumazenil. Flumazenil is a specific benzodiazepine antagonist and it is used to reverse the effects of benzodiazepines, including the life-threatening effects such as severe sedation, respiratory depression, and unconsciousness. It acts by competing with benzodiazepines for their binding sites on the GABA-A (gamma-aminobutyric acid type A) receptor complex, thereby reversing their central nervous system depressant effects.