The authorisation for the expansion of the International Security Assistance Force (ISAF) was extended for a year beyond October 13.
The ISAF has close to 40,000 troops in Afghanistan since the Taliban rulers were toppled in 2001.
The US maintains about 13,000 troops in a separate counter-insurgency force.
The council voted 14-0 with Russia abstaining because of a reference to Japan's naval mission supporting US-led forces in Afghanistan, an issue which has caused a political storm in Japan.
Vitaly Churkin, Russia's UN ambassador, said the resolution "should not have given priority to domestic considerations".
China also criticised the resolution, although it voted in favour.
The move comes as Nato forces launched a major operation in southern Afghanistan to clear Taliban fighters from one of the most violent provinces in the country.
About 2,500 soldiers were deployed to Helmand's upper Gereshk valley, where violence has soared this year with daily clashes throughout the summer.
Wednesday's resolution also recognised the need to further strengthen ISAF, asking countries "to contribute personnel, equipment and other resources".
The council strongly condemned suicide attacks, abductions and other violence against civilians and international forces.