Most of the visitors' early chances came from moves down either flank and the Eagles were fortunate to survive when ClaudeDavis beat Richard Dunne to Emile Heskey's knockdown.
Mark Noble surged into the box, only to be denied by a brave tackle from ClaudeDavis, who was injured in the process and had to be replaced by Chris Morgan.
Steven Whittaker's header over the crossbar from Steven Davis' cross failed to worry the Zenit goalkeeper before striker Jean-Claude Darcheville was tripped by Denisov and Rangers were awarded a free-kick on the edge of the area.