It all happened at El Divino Salvador Presbyterian Church on Enchandia Street.
A man just released from Twin Towers jail was being taken by private ambulance to the hospital.
En route to Los Angeles County-USC Medical Center, authorities said the man attacked a medic and commandeered that ambulance, then crashed it near the church.
He ran into the church where the standoff began, and injured at least one officer as they brought in canine units.
"While they were searching for the guy, apparently this suspect armed himself with a butcher knife from the kitchen in the rectory of the church and ended up stabbing one of our officers in the left bicep," LAPD Cmdr. Andrew Smith said.
The injured officer's partner shot and killed the suspect. Police said the officer is going to be OK.