After a 0-0 draw in Lyiv, the tie was on a knife edge coming into the game in Gelsenkirchen.
However, goals from Marlos, Facundo Ferreyra and Viktor Kovalenko meant that the dreams of a European trophy was over for the Royal Blues.
Marlos breaks the deadlock
The opening stages of the game were fast-paced and frantic. Schalke had good chances through Johannes Geis and Younes Belhanda, but the post denied the former's free-kick and the Dynamo Kiev loanee couldn't find a way past Pyatov. The visitors also came close through Dario Srna and Taison, though they would eventually get their reward.
Shakhtar's first goal with a thing of beauty. After Leroy Sané gave the ball away, a hopeful clearance found Kovalenko darting up the pitch. He managed to evade several tackles before slipping in Ferreyra. The Argentine cut back towards Marlos, who produced a fantastic pirouette back-heel to find the bottom corner.
Donetsk dash Schalke hopes
André Breitenreiter brought Sidney Sam, Dennis Aogo and Franco di Santo off the bench all within a few minutes of each other, in a bid to spark some life into their attack.
On the hour mark, di Santo wasted a huge chance after the failed to apply the necessary finish from just two yards out after Joel Matip flicked on Geis' corner.
Just three minutes later, Schalke were down and out as a Taison cross was finished off by Ferreyra. The home fans were far from pleased, as their rotten run continued.
Kovalenko heaped further misery on the Schalke support, who are unable to shake their topsy-turvy form, by slamming home off the underside of the bar.