Cars packed with explosives targeted a police headquarters and an air-security intelligence centre at 7.30am, television said, shredding the facade of one building and sending debris flying through the streets.
Gruesome images from the sites showed what appeared to be smouldering bodies in two separate vehicles, a wrecked mini-van smeared with blood, and severed limbs collected in sacks.
At least 27 people were killed and 140 wounded, an interior ministry statement said.
"We heard a huge explosion. At that moment the doors in our house were blown out ... even though we were some distance from the blast," said one elderly man, his head wrapped in a bandage.
No-one claimed responsibility for the explosions, which followed a series of suicide attacks in Damascus and Syria's second city Aleppo in the past three months.
The blasts came two days after the first anniversary of the uprising, in which more than 8000 people have been killed and about 230,000 forced to flee their homes.
They also coincided with a joint mission by the Syrian government, the UN and the Organisation of Islamic Co-operation that was due to start assessing humanitarian needs.
One source involved in the mission said team members were still gathering in Syria and it was not yet clear if they would begin their work this weekend as previously planned.
Violence was also reported elsewhere in Syria yesterday.
The British-based Syrian Observatory for Human Rights, which has a network of contacts in Syria, said the body of an old man was found a day after he was arrested in the northern Jabal al-Zawiyah region.
It added that five more died in the eastern town of Raqqa. One person was shot dead by security forces during the funeral of two people killed on Friday.
The Avaaz campaign group said it had evidence of 32 children being tortured last week in the central city of Homs, posting footage on the Internet of the infants in hospital. It said some had broken bones, badly cut fingers and gunshot wounds.
Syria denies accusations of brutality and says it is battling a foreign-backed insurgency. Reports cannot be independently verified as authorities have barred outside rights groups and journalists.
The UN-Arab League envoy for Syria, Kofi Annan, warned on Friday that the crisis could spill over into neighbouring countries and urged world powers to lay aside their differences and back his peace initiative.
While the West and much of the Arab world have lined up to demand Assad steps down, his allies Russia, China and Iran have cautioned against outside interference.
"The stronger and more unified your message, the better chance we have of shifting the dynamics of the conflict," an envoy said, summarising Annan's remarks to a closed meeting of the 15-nation Security Council.
Turkey has said it might set up a "buffer zone" inside Syria to protect fleeing refugees, while Annan will send a team to Damascus next week to discuss a proposal to deploy international monitors in the country.