A man posing as an exterminator stole cash and jewelry from several Brooklyn homes after persuading the residents to leave him alone in their bedrooms, police sources said yesterday.

But the super of one of the Brighton Beach buildings picked the fake bug killer from a photo array, and cops arrested Ahmad Rennick, 42, on charges of burglary and criminal impersonation.

Rennick — a former pest-control worker — allegedly struck apartments on Avenue Z, Sea Breeze Avenue and Brighton Seventh Street from Feb. 14 to Monday.

Armed with a bug sprayer, he targeted women’s apartments and made off with cash and jewelry, the sources said.