He said the men had driven their auto into the police yard before getting out to stage the attack.
"Three officers were injured and one later died in hospital", said local police chief Nandang, who goes by one name.
The driver of the van then attempted to the flee the scene, hitting and killing one police officer, he added.
The attacks have put Indonesia on edge as the world's biggest Muslim majority country starts the holy fasting month of Ramadan from Thursday.
"The one who escaped has been captured and secured at Pekanbaru police station", Mr Wasisto said.
Earlier, an internal police report said one of the dead men had a suspected bomb strapped to his body.
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Police have been frequent targets of mostly low level attacks by local militants, including a 2017 suicide bombing at a bus station in Jakarta that killed three police officers.
It comes after a series of suicide attacks carried out by families that have shocked the country. "People wearing masks alighted from a van and stabbed a police officer nearby", Doddy said as quoted by tribunnews.com.
The church bombing family were in the same religious study group as the Surabaya police station bombers and a third family believed to be linked to the wave of attacks, authorities said.
On Monday, a family of five, including an eight-year-old child, mounted a suicide bombing at the Surabaya police headquarters, injuring 10 people.
The coordinated church attack was a sign local extremist groups were becoming more proficient, and stirs concerns about an uptick in extremism as hundreds of Indonesians who flocked to fight alongside Islamic State in the Middle East return home.