Los Blancos entered the match as the firm favourites to advance into the quarter-finals following a 6-1 win when the pair met in the first leg last month.
Cristiano Ronaldo made it 1-0 on the night after 21 minutes, but Tim Hoogland levelled for the visitors just past the half-hour mark. Madrid emerged victorious on the night, however, following second-half goals from Ronaldo and Alvaro Morata.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
MADRID: Casillas; Nacho, Ramos, Varane, Coentrao; Illarramendi, Alonso, Isco; Ronaldo, Morata, Jese
SCHALKE: Fahrmann; Hoogland, Howedes, Matip, Kolasinac; Ayhan, Neustadter; Obasi, Meyer, Draxler; Huntelaar
12 – Bayern Munich recorded the biggest aggregate win in a Champions League knockout game (12-1): 0-5 & 7-1 vs Sp. Lisbon in 2009. Challenge— OptaJose (@OptaJose) March 18, 2014
134 - Iker Casillas already played 134 times in the CL, the entire starting XI of Schalke only 118 times. Experience.— OptaFranz (@OptaFranz) March 18, 2014
12 - Cristiano Ronaldo has now matched his best goals return in a single Champions League season (scored 12 last season). Routine.— OptaFranz (@OptaFranz) March 18, 2014