Real's galactico-laced frontline of Karim Benzema, Gareth Bale and Cristiano Ronaldo scored two goals each as the Spaniards secured only their second win in 26 trips to Germany and effectively booked their spot in the last eight.
Fernando Torres's early goal for Chelsea was cancelled out by Galatasaray's Aurelien Chedjou in the second half.
Benzema opened the scoring for Real Madrid on 13 minutes after Bale and Ronaldo had caused mischief in the German defence and Wales winger Bale drove through the heart of the Schalke backline to double the lead eight minutes later.
Ronaldo scored seven minutes after the break with a left-footed effort after a series of stepovers bamboozled Schalke's Joel Matip and Benzema grabbed his second following a one-two with Ronaldo.
Bale made it 5-0 with a precise finish after being played through by Sergio Ramos and Ronaldo netted for the 11th time in this season's competition before former Real striker Klaas-Jan Huntelaar grabbed a stoppage-time consolation for the hosts.
In Istanbul, Galatasaray striker Didier Drogba was reunited with his former club but he suffered a largely frustrating evening leading the line for his new side.
Chelsea took the lead when Torres scored the first goal by an English club in this season's last-16 first legs, side-footing into an empty net from close range after nine minutes.
Chedjou equalised after 64 minutes when he tapped in after Wesley Sneijder's corner was missed by John Terry.
The return legs will take place on March 18.
(Editing by Ed Osmond)
