Power said passage of Resolution 2133, which calls on member nations to prevent the payment of ransom to terrorists, would undermine the "business model" used by terror groups.
She said terrorist groups have collected more than $120 million in ransom payments during the last 10 years.
"Extracting ransom through kidnapping is today's most significant terrorist financing threat because it has proven itself a frighteningly successful tactic," she said in a statement Monday. "Every ransom paid to a terrorist organization encourages future kidnapping operations."
The resolution -- passed unanimously during a Monday vote by the 15-member Security Council -- is the first resolution ever devoted specifically to kidnapping for ransom by terrorists.
British Ambassador to the United Nations Mark Lyall Grant, who helped draft the measure, said in a statement the resolution breaks a cycle that gives terrorists the money they need for potential future operations.
Resolution 2133 calls on member states to encourage the private sector to not bow to terrorist demands for ransom.