ISIS fighters were responsible for the blasts near the capital Damascus and in third city Homs.
Citing a security source, IS's propaganda agency Amaq said IS fighters were responsible for the blasts near the capital Damascus and in third city Homs.
Syria's state news agency SANA said the explosions in both areas were caused by security forces firing on the cars as they approached checkpoints.
The first explosion killed four people and wounded 30 near the Al-Zahraa neighbourhood of Homs city, SANA said.
Most residents of Al-Zahraa belong to the same Alawite sect as President Bashar al-Assad, and the district has been repeatedly targeted by IS.
The two bombers drove the vehicle towards a checkpoint where security forces opened fire, detonating the explosives inside, SANA reported.
"Some of those with minor injuries have already left hospital," Homs governor Talal Barazi told state television.
The second blast claimed by IS took place on the road south from the capital to Syria's holiest Shiite Muslim shrine, the Sayyida Zeinab mausoleum.
Police opened fire on a vehicle near a checkpoint which turned out to be carrying explosives and blew up, killing one civilian and wounding another, SANA said.
In March, twin suicide attacks at Sayyida Zeinab killed 74 people, most of them Iraqi pilgrims.
Tuesday's bombings come two days after the government announced it had taken full control of Homs, following the evacuation of rebels from the last neighbourhood under their control.
The Russian-supervised evacuation from the Waer district was the latest blow to the rebels by government troops backed by their Russian and Iranian allies.
Since December, the rebels have lost their former bastion of Aleppo and nearly all of the areas they controlled in Damascus.
More than 320,000 people have been killed since Syria's conflict broke out in March 2011 with protests against Assad's rule.
Millions more people have been displaced.