The two sides headed into the clash level, having played out a goalless draw in the first leg in Istanbul the week before.
However, Shakhtar made easy work of the visitors in the end, with Olexandr Gladkiy, Dario Srna and Alex Teixeira making the difference in Ukraine to win the tie for Mircea Lucescu's men.
While there was no Robin van Persie in the Fener side, Vitor Pereira's men boasted the likes of Diego, Raul Meireles, Nani, Simon Kjaer and Bruno Alves, but they were second best to their hosts from the beginning.
Indeed, Shakhtar almost took the lead within 40 seconds when Marlos received the ball on the right side, cut into the middle and smashed it towards goal, only to see it hit the side netting.
Fenerbahce's first real chance came 10 minutes into the clash, with Fernandao leaping up to head a cross towards goal, but it went over the bar.
Teixeira then had an opportunity at the other end, finding himself in space in the box but his effort was straight at the goalkeeper.
