Schalke booked their spot in the quarterfinals via the away goals rule after rallying for a 2-2 draw at Borussia Monchengladbach.
After drawing 1-1 in Gelsenkirchen, goals from Andreas Christensen in the 26th minute and Mahmoud Dahoud in the 45th looked to have the hosts on their way.
However, Leon Goretzka pulled a goal back nine minutes after the break and a Nabil Bentaleb penalty sealed Svchalke's passage into the next round.
Lyon also advanced, holding on to get through 5-4 on aggregate despite a 2-1 loss at Roma.
The French side carried a 4-2 lead into the Estadio Olimpico and an early goal from Mouctar Diakhaby gave the hosts an uphill climb.
Kevin Strootman struck back in the 17th minute and a Lucas Tousart own goal at the hour mark complicated the tie, but Lyon held on to reach the last eight of the competition.