The US says an independent Palestinian state should be established through direct negotiations between Israel and the Palestinian Authority and not through UN action.
It vetoed a draft resolution on Thursday that recommended to the 193-member UN General Assembly that "the State of Palestine be admitted to membership of the United Nations".
Britain and Switzerland abstained, while the remaining 12 council members voted yes.
The Palestinians are currently a non-member observer state, a de facto recognition of statehood that was granted by the UN General Assembly in 2012.
But an application to become a full UN member needs to be approved by the Security Council and then at least two-thirds of the General Assembly.
The Palestinian push for full UN membership comes six months into a war between Israel and Hamas in Gaza, and as Israel is expanding settlements in the occupied West Bank.
"Recent escalations make it even more important to support good-faith efforts to find lasting peace between Israel and a fully independent, viable and sovereign Palestinian state," UN Secretary-General Antonio Guterres told the council earlier on Thursday.
"Failure to make progress towards a two-State solution will only increase volatility and risk for hundreds of millions of people across the region, who will continue to live under the constant threat of violence," he said.
Israel's UN Ambassador Gilad Erdan said Palestinians failed to meet the criteria to become a full UN member, which he outlined as: a permanent population, defined territory, government, and capacity to enter relations with other states.
"Who is the council voting to 'recognize' and give full membership status to? Hamas in Gaza? The Palestinian Islamic Jihad in Nablus? Who?" Erdan asked the Security Council earlier on Thursday.
He said granting full UN membership to Palestinians "will have zero positive impact for any party, that will cause only destruction for years to come, and harm any chance for future dialogue".
The UN Security Council has long endorsed a vision of two states living side by side within secure and recognised borders. Palestinians want a state in the West Bank, east Jerusalem and Gaza Strip, all territory captured by Israel in 1967.
The Palestinian Authority, headed by President Mahmoud Abbas, exercises limited self-rule in the West Bank. Hamas ousted the Palestinian Authority from power in Gaza in 2007.
Ziad Abu Amr, special envoy of Abbas, earlier asked the US: "How could this damage the prospects of peace between Palestinians and Israelis? How could this recognition and this membership harm international peace and security?"
"Those who are trying to disrupt and hinder the adoption of such a resolution ... are not helping the prospects of peace between Palestinians and Israelis and the prospects for peace in the Middle East in general," he told the Security Council.
Abu Amr said full Palestinian UN membership was not an alternative for serious political negotiations to implement a two-state solution and resolve pending issues, adding: "However, this resolution will grant hope to the Palestinian people hope for a decent life within an independent state."
