State television showed thousands of people queuing to vote, as well as crowds waving Syrian flags.
Pictures sent by activists showed burnt cars, charred corpses and body parts in the area.
Officials said the election was a sign Assad was unwilling to seek a political solution to the conflict.
The UN's human right chief said violations by Syrian forces far outweighed those by the opposition.
Despite causing a civil war which has killed more than 140,000 people, Assad wants a third term.
The resolution called for the immediate lifting of sieges in specific towns and cities.