The four perpetrators on two motorbikes died after driving into the building gateway and detonating explosives, according to police, who said an 8-year-old girl on one of the motorcycles was thrown from the vehicle but survived. No fatality among the police officers but four were injured.
Christians are calling for prayer after several churches were attacked in Indonesia - with a single family suspected of carrying out the bombings.
The coordinated bombings on Sunday, followed on Monday by a suicide attack by another family on police headquarters in Surabaya, have horrified Indonesians who typically see their Muslim-majority country as diverse and tolerant.
A Surabaya police spokesman said police arrested 13 suspects over the two suicide bombings carried out by two families, after conducting raids in Surabaya and its neighbouring cities of Malang and Pasuruan.
On Sunday night, a bomb in the Wonocolo low-priced housing complex in Sidoarjo exploded prematurely, killing a woman and her 17-year-old child, police said.
"Following the attack, people are more cautious".
Officials have identified Oepriarto as the head of Jemaah Ansharut Daulah (JAD), an Indonesian IS-inspired network.
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Such groups, which are loyal to the Islamic State in Iraq and Syria, as well as returnees from ISIS territories in the Middle East, pose a growing new threat in Indonesia, said Mr Evan Laksmana, a senior researcher at the Jakarta-based Centre for Strategic and International Studies. "If three families can be involved in two days' worth of terrorist attacks in Surabaya, surely there are more ready to act".
THE Department of Foreign Affairs says it "continues to receive information" terrorists are planning fresh attacks in Indonesia and has warned Australians to take particular care in the country over the next few weeks.
Another family reportedly attacked a police station this morning, wounding 10 people including police officers.
Terrorist in Indonesia made police their main target after a number of their leaders and fellow terrorist fighters were arrested or killed by special anti terrorist police squad.
"Don't hesitate to demand they step down from their positions to give a chance to those who are more reliable", said Rachland.
The daughters were aged 9 and 12, while the sons were 16 and 18 years old, respectively.
Television footage appeared to show a person on a motorcycle driving into the grounds of a church before a bomb was detonated.