It also warned that it would "consider further steps" against the regime of President Bashar al-Assad unless Syria ends violence and complies with a ceasefire and six-point peace plan drawn up by the Arab League and UN envoy Kofi Annan.
The resolution is the first to be passed by the Security Council since the Syrian crisis -- which has pushed the country to the brink of civil war -- began over a year ago.
Significantly, it won the support of Russia and China, who had controversially vetoed previous resolutions aimed at bringing to an end the violence that has claimed 9,000 lives in the past 13 months.
Russia's UN ambassador, Vitaly Churkin, said Moscow was satisfied with the latest western-Arab resolution authorising the deployment of the first batch of unarmed UN observers to Syria to monitor its fragile truce.
Speaking after the vote, however, Mr Churkin warned against "destructive attempts at external interference" in Syria.
The vote came as the fragile ceasefire that has been in force for three days was rocked by fighting in Homs, where regime forces shelled rebel-held neighbourhoods.
Rebel fighters were also reported to have fired rocket-propelled grenades at an area held by regime loyalists.
The two sides have traded allegations of violations of the truce since it took effect formally last Thursday.
However, yesterday's reports of the use of heavier weapons suggested that the ceasefire was in jeopardy.
A video, shot in a destroyed part of what the cameraman said was the Homs neighbourhood of al-Qarabis, showed two tanks rushing through the streets to the sound of heavy gunfire and explosions.
"Look with your own eyes. Look, world. Watch what they are doing," the man making the video screams as a tank raises its turret.
The Syrian state news agency Sana said "armed terrorists" killed five people in ambushes around the country yesterday and kidnapped a parliamentary candidate.
Since the truce brokered by Mr Annan came into effect, fewer deaths have been reported. The UK-based Syrian Observatory for Human Rights said the shelling yesterday morning in Homs lasted for about an hour and there were no reports of casualties.
Activist Tarek Badrakhan in the Homs neighbourhood of Khaldiyeh, as well as Observatory monitors, said the shelling targeted the neighbourhoods of Jouret el-Shayah and Qarabees.
"I can see black smoke billowing from a building that was hit in Jouret el-Shayah," Mr Badrakhan said.
The Local Co-ordination Committees activist group said troops fired at a funeral in Aleppo. The Syrian Observatory said three people were wounded.
Meanwhile, troops were conducting a wave of arrests in the Damascus suburb of Dumair when a car exploded, killing one civilian and wounding two others, the Observatory said.