The adoption on Friday coincided with the scheduled implementation of the cessation of hostilities agreement reached by Russia and the US, Xinhua reported.
According to the deal, the halt was to begin at midnight (Damascus time) on Friday in the middle of the council session.
"It's zero hour, Damascus time," Japanese Ambassador Motohide Yoshikawa said as the clock struck within a minute of the scheduled starting time.
The new council resolution welcomed a February 11 statement from the 17-member International Syrian Support Group (ISSG) that seeks humanitarian aid access to Syria and a halt in fighting.
The resolution also demanded the implementation of a previous council resolution on Syria adopted on December 18, 2015, which called for an end to attacks on civilians and infrastructure as well as a political settlement of the crisis.
Before the resolution was voted on, Staffan de Mistura, the UN special envoy for Syria, spoke to the 15-member panel via teleconference from Geneva.
"This council meeting has a special significance on this exceptional day and night for the Syrians," he said.
"We now have specific obligations for ISSG members and for Syrians to fulfill," the envoy said. "There is a mechanism to that effect. There is an agreed set of actions and an immediate timeline."
"We are now at a crossroad -- we have the possibility to turn the page in the Syrian conflict -- after almost five years of one of the bloodiest conflicts in recent years," de Mistura said.
"It is potentially a historic junction to bring an end to the killing and destruction and to start a new life and hope for the Syrians," he said.
De Mistura also announced that a new round of Syria talks will be held on March 7.
The UN-mediated Syria peace talks, aimed at brokering a political solution between Syrian warring factions -- Syrian president Bashar al-Assad's government and opposition forces -- halted on February 3 after parties failed to see eye to eye on a number of issues.
US Ambassador Samantha Power was the first to speak after the 15-0 vote at the UN Security Council.
"The resolution we have just adopted... offers a genuine opportunity to pause, at least in part, the fighting in one of the most brutal conflicts the world has seen in a generation, and it's our best chance to reduce the violence," she said.
Russian Deputy Foreign Minister Gennady Gatilov said the measure "must be strictly implemented and without any preconditions" and "the process of implementation itself must be monitored reliably."
"As was confirmed in the joint statement of Russia and the United States, the Cessation of Hostilities regime will not apply to the Islamic State and Al-Qaeda-linked al-Nusra and other terrorist organisations that have been recognised as such by the UN Security Council, the combat against them will continue."
"Our position is that long-term stabilisation of Syria is impossible without eliminating the terrorist threat in this country," Gatilov said.
For his part, Syrian Ambassador to the UN Bashar al-Ja'afari said Damascus considers the Russian-US deal "as an important step toward a political settlement and affirms its willingness to contribute to the implementation of the Cessation of Hostilities."
The UN estimates that the Syrian crisis has claimed more than 250,000 lives since it broke out in March 2011.(IANS)