While the level of attacks in Anbar has declined, security in the province remains precarious.
Two other car bombs blew up in the city of Falluja, about 50km west of Baghdad, killing at least four people and injuring 21.
Police said one car bomb was left behind by gunmen who robbed a currency exchange merchant of $85,000 at his home.
The other exploded near a police patrol. A police source said the blast killed two people and wounded 11 others.
Meanwhile, the death toll from a spate of blasts in Iraq's southern port city of Basra on Saturday has risen to 43.
"We received 43 corpses, and 185 people have been wounded," Dr Riyadh Abdelamir, the director of Basra province's health department, said.
He said that women and children were among the wounded in Saturday's attacks.
Ali al-Maliki, the head of the Basra provincial council's security committee, on Sunday said the blasts had been caused by a double car bombing and a third roadside bomb which caused a large fire in crowded Ashaar market in Iraq's second largest city.
The city's police command had late Saturday attributed the explosion to the short-circuit of a communal power generator.
Overall violence in Iraq has ebbed since the peak of sectarian warfare in 2006-07 but bombings and suicide attacks occur regularly across the country.
Iraq has the world's third-largest reserves and many of the oilfields are located around Basra.
Nearly 400 civilians were killed in bombings and other attacks in July, almost double the June toll, Iraqi authorities say.
Tens of thousands of people were killed during the height of Iraq's sectarian slaughter in 2006-07.