The major powers overcame a prolonged deadlock to approve the council's first resolution on the Syrian conflict, which the UN says has left more than 100,000 dead in 30 months.
UN leader Ban Ki-moon called the "historic" resolution "the first hopeful news on Syria in a long time."
Resolution 2118, the result of bruising negotiations between the United States and Russia, gives international binding force to a plan drawn up by the pair to eliminate President Bashar al-Assad's chemical arms.
There are no immediate sanctions over a chemical weapons attack confirmed by the UN. But it allows for a new vote on possible measures if the Russia-US plan is breached.
US President Barack Obama hailed the resolution as a "potentially huge victory for the international community." He said before the vote that there would be "consequences" for any failure by Assad to keep a promise to follow the plan.
Russia, Assad's main ally, rejects any suggestion of sanctions or military force against Assad. It has already used its veto power as a permanent Security Council member to block three western drafted resolutions on Syria.
Russian Foreign Minister Sergei Lavrov stressed that there was no automatic enforcement and that any violations would have to be "carefully" considered by the Security Council.
The resolution "condemns in the strongest terms any use of chemical weapons in the Syrian Arab Republic, in particular the attack on August 21, 2013, in violation of international law."
The United States says the attack on the Damascus district of Ghouta left more than 1,400 dead. It blamed Assad's government for the sarin gas assault and threatened a military strike over the attack.
The council said it "decides, in the event of non-compliance with this resolution, including unauthorized transfer of chemical weapons, or any use of chemical weapons by anyone in the Syrian Arab Republic, to impose measures under Chapter VII of the United Nations Charter."
The charter can authorize the use of sanctions or military force. But diplomats said Russia would fiercely oppose any force against its ally.
Russia also rebuffed calls by European powers Britain and France for the Ghouta attack to be referred to the International Criminal Court.
The resolution expresses "strong conviction" that those responsible for chemical weapons attacks in Syria "should be held accountable."
The resolution formally endorsed a decision taken hours earlier by the Organization for the Prohibition of Chemical Weapons to accept the Russia-US disarmament plan.
The plan calls for all Syrian chemical weapons to be put under international control by the middle of 2014. Experts say the timetable is very tight.
International experts are expected to start work in Syria next week. Ban also told the Security Council he wanted to hold a new Syria peace conference in November.
"We are aiming for a conference in mid-November," Ban said. The UN leader said that the foreign ministers of Britain, China, France, Russia and the United States had agreed to make sure the two sides in the conflict negotiate in "good faith."
A first peace conference was held in June 2012 but there has been no follow-up because of divisions in the Syrian opposition and the international community.
Ban will begin contacts with his Syria peace envoy Lakhdar Brahimi next week on setting the firm date and who will attend the new meeting, diplomats said.
The 2012 conference among the major powers agreed that there should be a transitional government in Syria with full executive powers.
It also determined that there should be a new conference to decide how to implement the accord.
