History did not provide much inspiration for the Spanish giants, who had won on only one of their last 25 visits to face German opposition in UEFA competition, but their forwards were in imperious form at the Veltins Arena to give them what, barring a minor miracle, will prove an unassailable advantage to take into the second leg.
Karim Benzema gave them the lead with an emphatic 13th-minute finish and although Julian Draxler and Max Meyer then missed in quick succession for the hosts, Real were in control.
A second arrived through Gareth Bale, with the world's most expensive player netting a delightful solo goal before Cristiano Ronaldo - back in the side after a domestic three-match ban - scored his 10th Champions League goal of the season.
Benzema added his second of the day to make it 4-0 and then Bale scored again with just over 20 minutes remaining.
There was even still time for more late drama as Ronaldo scored his second of the night and Klaas-Jan Huntelaar gave the Germans what was scant consolation.
Schalke coach Jens Keller had spoken in the build-up about the Germans' need to be "brave" against a side he ranks as arguably the second best in the world - behind Schalke's Bundesliga rivals Bayern Munich - but there was little his side could do about Real's opener.
Ronaldo's attempted backheeled pass was deflected into the area for Benzema and the Frenchman coolly slotted past Ralf Fahrmann to give the visitors a perfect start.
Schalke should have levelled a minute later, however.
Draxler darted in behind the Real defence to direct Jefferson Farfan’s right-wing cross past Casillas, but the Spaniard launched himself across goal to palm it away, before Meyer blazed the rebound over.
Real made the most of that let-off and doubled their lead 21 minutes in, with Bale showing his class.
After cutting in from the right, the Welshman cleverly slalomed his way between Felipe Santana and Sead Kolasinac before squeezing a shot into the bottom-right corner, capping a wonderful solo run.
Ronaldo almost made it 3-0 just after the half-hour mark, but after jolting past Kolasinac and shooting from 20 yards, his low drive came back off Fahrmann’s right-hand post.
Ronaldo finally got a deserved goal in the 52nd minute and he netted in style as the Ballon d'Or winner dazzled Joel Matip with three stepovers before charging into the area and rifling in a left-footed effort.
A fourth arrived just five minutes later as Benzema doubled his tally for the match, passing into an empty net after playing a one-two with Ronaldo and bursting around Fahrmann, but things soon got even worse for the hosts.
With 21 minutes remaining, Bale raced on to an intricate throughball from Sergio Ramos and confidently caressed the ball past the goalkeeper with his left foot.
The visitors added a sixth for good measure as Ronaldo latched on to Benzema's pass, skipped past Fahrmann and passed home.
There was still time for Schalke to get a consolation as Huntelaar fired in a superb volleyed effort from the edge of the area, but Real had already long since killed off the tie.
