The nine-time winners had only won once before in 25 trips to Germany but victory was never in doubt at the Veltins-Arena with Real's most potent attacking weapons coming to the fore.
Karim Benzema, Gareth Bale and Cristiano Ronaldo all scored twice as an insatiable Madrid left Schalke requiring a miracle at the Bernabeu in three weeks time despite Klaas-Jan Huntelaar scoring the goal of the night in time added-on.
Schalke won a corner in the first minute and nearly took the lead but captain Benedikt Howedes' header from distance drifted wide of Iker Casillas' right-hand post.
But Real were seeing more of the ball and soon had the lead thanks to that potent attacking trio in the 13th minute.
Bale cut in on the right and found Ronaldo whose backheel took a deflection which found Benzema on the penalty spot and he made no mistake with a crisp finish.
They would not have it all their own way initially, though, and Schalke were almost level within two minutes.
Jefferson Farfan got down the right and his cross found Julian Draxler six yards out but Casillas was on hand to make a stunning reflex save.
Schalke were playing their part but it was 2-0 in the 21st minute thanks to the quick feet of Bale.
Benzema robbed Felipe Santana of possession and when the Welshman gathered the ball up he danced forward, beating two men before unleashing a quick shot which went in off the near post.
Real were building pressure and Ronaldo was clearly keen to get in on the goalscoring act as he brought down an Angel Di Maria pass and surged forward but his shot from the edge of the area came back off the post and safely into the arms of Ralf Fahrmann.
The visitors were now looking a threat every time they came forward and Ronaldo looked certain to score as he latched onto Di Maria's through-ball but Fahrmann did well to save with his feet.
Schalke were under fire as the break approached as first Benzema fired wide from Marcelo's cross and Fahrmann made another close-range save from Ronaldo but they made it to the interval without sustaining further damage.
The home side desperately needed to find something in the second half and Kevin-Prince Boateng forced Casillas into a save from long range in the 47th minute with Max Meyer horribly miscuing his effort on the follow-up.
But it was 3-0 in the 52nd as Ronaldo got the goal he had been so close to before the break. Bale played the ball across to the Portuguese on the left and he dazzled Joel Matip with two step-overs before firing low past a helpless Fahrmann.
Five minutes later it was four as Ronaldo and Benzema exchanged passes, with the former Manchester United man releasing his team-mate in the box to fire across the goalkeeper and into the far corner.
Real looked to be taking their foot off the gas after the goal and allowed Schalke to have possession but it was not long before Bale had his second of the night in the 67th minute.
Sergio Ramos gathered a loose ball in midfield and freed Bale on the right with the former Tottenham man doing well to keep onside and calmly lift the ball over Fahrmann.
Ronaldo was not to be outdone and had his brace in the 88th minute as substitute Isco and Benzema combined to release him and he calmly slotted past the keeper.
There was still time for former Real striker Huntelaar to net a stunning consolation when he volleyed home from the edge of the area after Christian Fuchs' cross to see Casillas beaten for the first time in ten appearances, but it is likely to be of little consequence.
Torres leads Chelsea in Gala draw
Chelsea may well be frustrated not to leave Turkey victorious but Fernando Torres' away goal in Galatasaray's cauldron of noise gives Jose Mourinho's men a decent chance of reaching the Champions League quarter-finals.
Having seen Manchester United follow Arsenal and Manchester City in losing their last-16 first-leg ties 2-0, the west Londoners refused to wilt under the intense pressure brought by the raucous Turk Telecom Arena crowd.
The Blues had looked on course for victory after Torres netted in a dominant first-half display, only for Roberto Mancini's side to produce a much improved performance after the break and earn a 1-1 as poor defending allowed Aurelien Chedjou to strike home.
This was a match of many a sub-plot, varying from Chelsea favourite Didier Drogba facing his former club for the first time to former Manchester City boss Mancini coming up against Mourinho, the man who succeeded him at the Inter Milan helm.
Mourinho named an attack-minded line-up and was rewarded after just nine minutes when fine play down the left ended with Fernando Torres sweeping home Cesar Azpilicueta's measured cross.
It was the first goal by an English side in Europe since 12 December and one Burak Yilmaz thought he had cancelled out as half-time approached, only for his strike from a quickly-taken throw-in to be disallowed as there were two balls on the pitch.
The other was under John Terry's arm and the Chelsea captain was booked for his part in the bizarre incident, which saw him booed off the pitch at half-time by the irate home support.
Galatasaray's fanatical support would soon be thanking Terry, though.
Minutes after Selcuk Inan hit the post, the Blues centre-back let Aurelien Chedjou out of his sights as he fired the hosts level to see the tie level when the teams resume battle in three weeks.