Klaas-Jan Huntelaar scored twice in the second half of extra time to complete his hat-trick and set up a return to his homeland where FC Schalke 04 will meet FC Twente in the round of 16.
The Netherlands striker ended FC Viktoria Plzeň's hopes of an upset raised when František Rajtoral cancelled out his early opener two minutes from time. That came despite Marek Bakoš being sent off on the hour, but in the end their hard work was undone by the prolific Dutchman.
Having won all four previous home matches against Czech opposition, there was cause for optimism among the home crowd. Injury ruled out Lars Unnerstall, Schalke's young goalkeeper; however in Timo Hidebrand, a time-served deputy was at hand. Plzeň, meanwhile, were shorn of captain Pavel Horváth through suspension and his absence was felt just eight minutes in.
Julian Draxler's 20-metre drive could only be parried by goalkeeper Marek Čech and Huntelaar pounced from close range to score. If the goal settled the home side's nerves, though, they were soon shaken from any comfort. Milan Petržela sprinted clear on the right before crossing to the far post for Daniel Kolář to send a bullet header against an upright. Despite that scare and without managing to create another genuine scoring chance, Schalke were the more assertive of the two sides.
The balance seemed to have tipped firmly in favour of the Königsblauen when Bakoš was ordered off, judged to have elbowed Kyriakos Papadopoulos. Plzeň appeared down and out until, with the end in sight, Benedikt Höwedes' clearance fell for Rajtoral, who lashed inside the near post.
Yet the ten men of Plzeň were unable to stem the tide. As pressure mounted, Chinedu Obasi's cross was headed in by Huntelaar on 106 minutes and the former AC Milan striker made sure with his third at the death.