Russia, Syria's veto-wielding ally, endorsed the measure as did the rest of the 15-member council, a rare display of unity over how to address the conflict, which has left more than 240,000 people dead.
Under discussion for months, the US-drafted resolution sets up a team of experts tasked with identifying the perpetrators of the chemical weapons attacks and paves the way for possible sanctions to punish them.
The United States, Britain and France have repeatedly accused President Bashar al-Assad's forces of carrying out chlorine gas attacks with barrel bombs dropped from helicopters.
Both Russia and the United States, divided over the war since it broke out, welcomed the resolution.
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"We need to bring the same unity to urgently find a political solution," US ambassador Samantha Power said, adding the resolution "sends a clear and powerful message."
In a tweet, she called the probe panel a necessary step toward "eventual accountability."
Russian ambassador Vitaly Churkin said the resolution was "a good example of political will, of the will to cooperate and of perseverance to come up with a good product."
It mandates the panel to "identify to the greatest extent feasible individuals, entities, groups or governments who were perpetrators, organizers, sponsors or otherwise involved in the use of chemicals as weapons" in Syria.
UN Secretary-General Ban Ki-moon is tasked with assembling the team within 20 days, working with the Organization for the Prohibition of Chemical Weapons (OPCW), which is based in The Hague.
The panel would present its first findings to the council 90 days after it begins its work, which would be for a duration of one year.
Getting the panel up and running will require several steps, each of which must be approved by the Security Council, giving Russia the opportunity to stonewall the investigation down the line, diplomats said.
Syria's UN ambassador Bashar Jaafari said his country's army "has never used and will never use chemical weapons."
He said extremist groups linked to al-Qaeda have done so, and he questioned the neutrality of previous on-the-ground probes by the UN and the OPCW.