Several students from an adjacent university were among the dead, with dozens of others wounded, while security forces shut down the neighbourhood to vehicle traffic and sought to defuse a suspected car bomb nearby.
The attacks come amid a surge in nationwide unrest, with May the country's deadliest month since 2008, that along with a prolonged political deadlock have stoked concerns that Iraq is moving back to the brutal communal violence that blighted it in 2006 and 2007.
Today's attacks struck at the Habib ibn al-Mudhaher husseiniyah, or Shiite Muslim religious hall, in north Baghdad. It lies next to the Imam al-Sadiq university, a private teaching institution.
Many victims were university students who were taking a break from studying for their exams to pray.
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"What sins did these innocent students commit?" asked Mustafa Kamil, a student who was about to leave the site of the attacks to visit the morgue to help identify the dead.
"A few minutes ago, I was standing with my friend, and he asked me to go pray together. But I told him I wanted to study some more, to be ready for our exams.
"He said, 'I am going to pray, God will help me succeed'. He went, and now he will never come back."
According to witnesses and officials, the bombers, who were dressed in suits, began by gunning down the building's guard, followed by the first attacker blowing himself up at the entrance to the hall.
Soldiers standing guard at the scene said the inside of the building was covered in blood, with the walls and ceiling badly damaged by ball bearings, used by the suicide bombers to maximise the bloodshed.
Meanwhile, bombings elsewhere in Baghdad and north of the capital in Salaheddin province killed two people and wounded six.