Adam Szalai's goal on the stroke of half time has given Schalke a 1-0 lead over PAOK Salonika on the night and a 2-1 aggregate advantage.
Schalke came close to opening the scoring in the second minute when Szalai broke free of the Salonika defence but he fired his shot wide.
Jermaine Jones found himself in plenty of space just a minute later, which prompted him to unleash a powerful effort that was well saved by Jacobo Sanz.
Salonika found it difficult to enjoy any long spells of possession as the German visitors asserted their dominance in midfield.
Former Chelsea winger Miroslav Stoch looked the most dangerous player for the hosts and he threatened to open the scoring in the 36th minute when he cut inside from the left wing before hitting a tame shot straight at Timo Hildebrand.
Schalke's superiority finally brought a breakthrough on the stroke of half time when Atsuto Uchida picked out Szalai, who fired home his effort to give the visitors the advantage.