A police officer rescued an injured man from a house fire Friday afternoon in Jersey City, officials said. The Jersey City officer, who was first on the scene of the blaze around 4 p.m., ran inside the burning Van Horne Street building and brought a man to safety, according to city spokeswoman Kim Wallace-Scalcione. The man suffered third-degree burns and was taken to a local hospital, Wallace-Scalcione said. Flames damaged the upper floors of five attached buildings near Bramhall Avenue, according to the spokeswoman, who said the fire was under control as of shortly before 6 p.m. The fire “ma…