Two bombs later went off in the eastern town of Muqdadiya, killing at least 20 people and wounding another 50, security and medical sources said. Another blast in a southeastern Baghdad suburb killed seven more.
Islamic State militants controlling swathes of Iraq's north and west claimed responsibility for the mall attacks, which it said had targeted a gathering of "rejectionist heathens", its derogatory term for Shi'ite Muslims.
The Iraqi government last month claimed victory against the hardline Sunni militants in the western city of Ramadi and have slowly pushed them back in other areas.
Monday's attacks left the biggest death toll in three months. Interior Ministry spokesman Brigadier General Saad Maan blamed "this terrorist group after they suffered heavy losses by the security forces", without naming Islamic State.
Seven people, including two policemen, were killed in the car bomb blast near the Jawaher mall in the predominately Shi'ite district of Baghdad Jadida, police and medical sources said.
Five more people were shot dead by the gunmen storming the mall, and six others were killed when those same assailants detonated their explosive vests, the sources said.
Police regained control of the mall, in the east of the city, and a senior security official told state television there were no hostages, rejecting reports that there had been people held.
"The security forces are at the scene and managed to recover the wounded. The situation is under control," Maan added.
As well as the violence meted out by Islamic State, Iraq is also gripped by a sectarian conflict mostly between Shi'ites and Sunnis that has been exacerbated by the rise of the militant group.
At least seven people were killed when a suicide bomber driving a car attacked a commercial street in a southeastern Baghdad suburb on Monday, police and medical sources said.
The blast in the Sunni district of Nahrawan left more than 15 people wounded, the sources added.
Earlier in the day, three people were killed and eight others wounded when a car bomb claimed by Islamic State went off near a restaurant in Baquba, 65 km (40 miles) northeast of Baghdad, security and medical sources said.
Two bombs later exploded in an area frequented by Shi'ite militia fighters in the town of Muqdadiya, another 15 km (10 miles) further northeast, security sources said.
At least 20 people were killed and 50 wounded in those blasts. A suicide bomber detonated his explosives-filled vest inside a casino in the town. A car bomb parked outside then went off as medics and civilians gathered at the site of the first blast.
Security officials said they had imposed a curfew for all of Diyala province, where Muqdadiya and Baquba are located.
There were no immediate claims of responsibility for the attacks in Muqdadiya and the Baghdad suburb.