The vote was 14-0, with the United States abstaining.
The vote followed three days of intense negotiations between ministers from key Arab nations and the council's veto-wielding Western powers - the United States, Britain and France. It came on the 13th day of an Israeli air and ground offensive against the Islamic group Hamas, which rules Gaza and has been launching rockets and mortars into southern Israel for years.
The United States, Israel's closest ally, and Arab nations that have close ties to Hamas negotiated the text of the resolution. But it will be up toand Hamas to decide to stop their military activities.
"We are all very conscious that peace is made on the ground while resolutions are written in the United Nations," British Foreign Secretary David Miliband said. "Our job here is to support the efforts for peace on the ground and to help turn the good words on paper into changes on the ground that are desperately needed."
The agreement came on the third day of an emergency council session demanded by the Arabs to try to end the fighting in Gaza.
Although passing a resolution at the U.N. doesn't guarantee that either Hamas or Israel will respect it, the vote means Arab League countries and the U.K. and France - which negotiated the deal - have agreed on the design for a cease-fire, reported CBS News foreign affairs analyst Pamela Falk at U.N. headquarters.
In addition to the cease-fire, the resolution calls for the unimpeded provision of humanitarian assistance in Gaza, the re-opening of border crossings, and a crackdown on arms smuggling to Hamas, added Falk. (Click here to read more analysis from Falk in World Watch.)
Israeli envoys went to Cairo, Egypt, on Thursday and held talks with Egyptian officials on an initiative by the presidents of Egypt and France that calls for a temporary truce. Hamas militants have yet to commit to coming to Cairo for talks and said they have major reservations about the plan.
Rice said the U.S. abstained - knowing that the resolution would pass - because the Washington wanted to see the results of the Egyptian mediation efforts, presumably meaning the Bush administration wanted to see if Hamas was on board with a cease-fire. Earlier in the day, Hamas officials rejected the Cairo proposal.
"The issue (for Israel) is how to keep Hamas from re-arming after any potential cease-fire," reports CBS News correspondent Mark Phillips from the Israel-Gaza border. "If they simply bring more weaponry in, the Israelis fear they will just be back here in six months having to do this all over again."
Hamas violently wrested control of the Gaza Strip from the Palestinian Authority in June 2007 and is considered a terrorist organization by the U.S. and Israel.
Israel's government said Wednesday that it viewed the Egyptian-French proposal positively but stopped short of acceptance.
Thursday night's resolution came during a week of rising Palestinian casualties in Gaza. The death toll topped 700 Palestinians Thursday, according to Gaza medical officials. Eleven Israelis have died since the offensive began on Dec. 27.
In Washington, the Senate unanimously adopted a resolution Thursday stating an "unwavering commitment" to Israel and its right to defend itself, while also calling for "a viable and independent Palestinian state living in peace alongside a secure state of Israel." The House was expected to pass a similar measure Friday.