Maccabi Haifa crashed out of the Europa League after losing their final Group J fixture to Schalke.
The home side knew a win would guarantee their place in the last 32 of the competition regardless of the result between Steaua Bucharest and AEK Larnaca, who started the evening one point behind.
But they never recovered from going behind to Jurica Buljat's own goal and, after Yaniv Katan's 72nd-minute penalty was saved, late goals from Ciprian Marica and Andreas Wiegel sealed the win for Schalke.
That meant Steaua advanced to the knockout stage instead courtesy of a 3-1 win at home to AEK.
Schalke were without coach Huub Stevens at the Qiryat Eliezer Stadium after he remained in Germany to be with his seriously ill mother.
And the German side were also without the likes of rested stars Raul, Klaas Jan Huntelaar and Jermaine Jones, but still proved worthy of their status as group winners.
They started well with Alexander Baumjohann volleying over in the third minute and took the lead in the eighth minute through Buljat's unfortunate own goal.
Marica sprung the offside trap and crossed towards Julian Draxler at the far post, with Buljat only able to guide the ball into his own net in attempting to clear the danger.
The home side tried to respond but Timo Hildebrand had a comfortable save from Vladimir Dvalishvili's 25-yard shot before Bojan Saranov had to make saves from Baumjohann and Draxler in quick succession at the other end.
Clear-cut chances were hard to come by until Maccabi were presented with a great opportunity to equalise in the 72nd minute when Alban Sabah was penalised for handball.
Katan stepped up to the spot but saw his penalty saved by Hildebrand and Schalke soon made the game safe.
In the 83rd minute Marica fired home from the right-hand side of the area and in the closing moments Wiegel completed the win with a third from 12 yards.