The resolution demanding the ceasefire "without delay" was adopted as Syrian government forces pounded the rebel-held enclave of Eastern Ghouta, where hundreds have died during a week-long assault.
"We are late to respond to this crisis, very late," US Ambassador Nikki Haley told the council after the vote, accusing Russia of stalling the vote.
More than 500 people, including more than 120 children, have been killed in seven days of relentless airstrikes in Eastern Ghouta, which UN Secretary-General Antonio Guterres described as "hell on earth."
The resolution demands a cessation of hostilities "without delay" throughout Syria to allow the "safe, unimpeded and sustained" deliveries of aid and evacuations of the sick and wounded.
To win Russia's approval, language specifying that the ceasefire would start 72 hours after the adoption of the draft was scrapped, replaced by "without delay," and the term "immediate" was also dropped in reference to the aid deliveries and evacuations.
Diplomats said they were confident that this would not open the door to postponing the ceasefire, as council members had made clear in negotiations that the truce must quickly come into force.
In another concession to Russia, the resolution said the ceasefire will not apply to operations against the Islamic State group or Al-Qaeda, along with "individuals, groups, undertakings and entities" associated with the terror groups.
That would allow the Syrian government offensive to continue against Al-Qaeda-linked jihadists in Idlib, the last province in Syria outside the control of Damascus.
The text demands the lifting of all sieges including in Eastern Ghouta, Yarmouk, Foua and Kefraya and order all sides to "cease depriving civilians of food and medicine indispensable to their survival."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)