Police say 52-year-old Semyom Levin, one of the victims, was found dead on the scene.
Police say Iglanov pointed his gun at his head and then turned the weapon at the officers, who were forced to open fire.
The man was suspected of pushing his way into an apartment and shooting a couple he used to work for, both computer technicians.
Levin's wife, 45-year-old Marina Tartakouskaya, was shot in the abdomen.
Levin was shot in the head.
They were both taken to Staten Island University Hospital. The woman was stable and expected to survive.