Rafik Hariri and 22 others died in February's blast in Beirut
However the resolution's sponsors - the US, France and the UK - dropped a specific threat of sanctions at the last minute in order to win support.
Instead, the resolution warns of "further action if necessary".
A UN inquiry into the killing of Hariri in February implicated Syrian and pro-Syria Lebanese officials.
Now the Syrian government needs to make a strategic decision to fundamentally change its behaviour
Condoleezza Rice
US Secretary of State
Syrians glued to debate Profile: UN Security Council
Russia and China had expressed deep concern that the sanctions against Syria proposed in an earlier draft of the resolution were too harsh, and the threat was removed in a subsequent version.
BBC Middle East analyst Roger Hardy says the Syrians may be relieved that the wording of the resolution has been softened, but the international community has nevertheless given them a stern warning that they must co-operate fully with the continuing inquiry into the Hariri affair.
The fact that there is a large degree of international consensus on the issue, he says, makes it harder for them to claim they are simply the victims of a bullying American superpower.
Suspects targeted
The killing of Hariri in a massive car bombing in Beirut earlier this year led to widespread criticism of Syria, which was forced to withdraw its soldiers from Lebanon as a result.
Syria is key to the Middle East - pressure on it will shift the last of the moderates to the extreme
Bill, US
Syria crisis: Your views
A UN inquiry was also launched in the aftermath.
Last week, its lead investigator, Detlev Mehlis, said Syria had given misleading information and had not fully co-operated with his commission.
The brother and brother-in-law of Syrian President Bashar al-Assad were among the suspects named in an unedited version of Mr Mehlis's report.
The Security Council resolution says that anyone suspected of being involved with Hariri's murder should be arrested and made available for questioning.
They would also be banned from travelling and have their assets frozen.
KEY UN FINDINGS Assassins had considerable resources and capabilities Evidence suggests both Syria and Lebanon were involved Crime was prepared over several months Hariri's movements and itineraries were monitored Highly unlikely Syrian or Lebanese intelligence were not aware of assassination plot UN report in full (488K) Most computers will open PDF documents automatically, but you may need to download Adobe Acrobat Reader. Download the reader here
Speaking in the council after the vote, US Secretary of State Condoleezza Rice said: "With our decision today, we show that Syria has isolated itself from the international community through its false statements, its support for terrorism, its interference in the affairs of its neighbours and its destabilising behaviour in the Middle East.
"Now the Syrian government needs to make a strategic decision to fundamentally change its behaviour."
UK Foreign Secretary Jack Straw said Syria's attitude to date had been "grudging and evasive", and that Damascus had now been put on notice that the UN's patience had limits.
"Failure to co-operate fully and now will oblige us to consider further actions to ensure that the Security Council... can play its part in the Lebanese government's determination to see justice done."
But Chinese Foreign Minister Li Zhaoxing cautioned that the Mehlis report was still a preliminary report.
"The commission itself believes that the investigation is yet to be completed and there is no final conclusion," he told the council.
"Under such circumstances it is inappropriate for the council to prejudge the outcome of the investigation and to threaten to impose sanctions."
Syrian inquiry
Responding to the vote, the Syrian government insisted it had co-operated fully with the UN investigation.
At the weekend, Syria announced its own inquiry into the death of Hariri.
Damascus said a special judicial committee would question both civilian and military personnel in the country.
The committee would also co-operate with the UN investigation, the Syrian presidency said.
Der UN-Sicherheitsrat hat in seiner heutigen Sitzung einstimmig eine Resolution verabschiedet, in der Syrien zur vollen Kooperation mit der UN-Sonderermittlungskommission zur Untersuchung des Hariri-Attentats vom Februar des Jahres aufgefordert wird.

In letzter Minute vor der entscheidenden Abstimmung hatten die Antragsteller – USA, Frankreich und Großbritannien – einen Passus der Resolution zurückgezogen, in der Syrien Sanktionen angedroht worden waren. Daher gelang es, im Sicherheitsrat bei der Verabschiedung Einstimmigkeit zu erzielen. Sogar Russland und China stimmten für die Resolution.

Rafiq Hariri war der ehemalige libanesische Präsident, der am 14. Februar 2005 in Beirut einem Bombenattentat zum Opfer gefallen war. Die UN hatte daraufhin eine Sonderkommission eingesetzt, die die Umstände seines Todes untersuchen sollte. Die Massenproteste im Libanon gegen die Ermordung Hariris und der internationale Verdacht, Syrien sei in das Mordkomplott verwickelt, hatten die syrischen Streitkräfte schließlich zum Rückzug aus dem Libanon gezwungen. Der Bericht der Sonderkommission unter der Leitung des deutschen Staatsanwaltes Detlev Mehlis war am 25. Oktober dem UN-Sicherheitsrat vorgestellt worden. Dabei hatte Mehlis keinen Zweifel daran gelassen, dass höchste libanesische und syrische Stellen vermutlich an der Attentatsplanung und -durchführung beteiligt gewesen waren. Eine gründlichere Untersuchung, die eindeutigere Beweise hätte liefern können, war unter anderem an der Weigerung Syriens zur vollen Kooperation mit der Sonderkommission gescheitert, wie Mehlis betonte.

Die jetzige Resolution fordert Syrien auf, mit der Sonderkommission besser zusammenzuarbeiten. Verdächtige im Zusammenhang mit dem Attentat sollen festgenommen und ihre Konten eingefroren werden, fordert der Sicherheitsrat weiter. Weitere Schritte behält sich der UN-Sicherheitsrat vor, wie in weiteren Stellungnahmen der Außenminister des Sicherheitsrates, Rice (USA) und Straw (Großbritannien), betont wurde.