A system and method for preventing a broken printing web from wrapping about or otherwise fouling the blanket cylinders of printing press units. The system and method includes a web tensioning device located downstream of the printing press units for maintaining tension upon a broken web and pulling the web from the printing press units. The device includes a plurality of web disturbance detectors for detecting a wave, ripple or other disturbance indicative of a web break. A pair of anti-wrap rollers located above and below the web are engaged upon detection of a web break to engage the web between them to exert tension onto the web and pull it from the printing units. The anti-wrap rollers are rotated at a surface speed nominally greater than the surface speed of the printing rolls. The anti-wrap rollers include a plurality of opposed peak and valley portions which enable them to interlock and grip the web along a line of contact.