A superb opener from Cristiano Ronaldo and a close-range second from Karim Benzema put los Blancos in the driving seat with a 2-0 lead at the Bernabeu before the half-hour mark.
And though Galatasaray showed some promise, Madrid were always the superior side, and Gonzalo Higuain came off the bench to nod home a third in the 73rd minute to make the second-leg at the Ali Sami Yen little more than a formality, barring a monumental collapse from Jose Mourinho's men.
Benzema was preferred to Higuain up front, while Michael Essien replaced Alvaro Arbeloa at right-back, and captain Iker Casillas was excluded from the squad altogether.
With only nine minutes on the clock, Madrid were ahead. Mesut Ozil was the architect, slipping in Ronaldo with a superb through ball, which was matched by an exquisite lob over Fernando Muslera.
Didier Drogba had a chance to respond after shaking off Raphael Varane with a powerful turn and squaring up to goal, but the Ivorian rather snatched at his shot and sent it high and wide.
There was real ebb and flow developing to the game, and the sprightly Ozil was denied from the edge of the box by Muslera, before Drogba’s swerving effort from distance was met with a safety-first punch from Diego Lopez.
But only one side were able to make their chances count, and Madrid gave another lesson in clinical finishing just before the half-hour mark. Essien’s cross was plucked from the air exquisitely at the far post by Benzema, who was then left with a simple tap-in.
Galatasaray, to their credit, or perhaps because they had no other option, kept pushing forward. Burak Yilmaz missed from close range after Drogba had bettered Sergio Ramos, and Emmanuel Eboue tested Lopez with a low drive following a one-two with the Ivorian striker.
But the hosts’ forays forward meant that the possibility of a third Madrid goal always existed, and after a cheap foul by Dany Nounkeu at the corner of the box, Ronaldo dipped the resulting free-kick onto the roof of the net shortly before the break.
But in sharp contrast to the enterprise that marked the first half, the second period progressed with a far more measured tempo from Madrid, who, with a two goal advantage in hand, seemed content to make the visitors chase the game by holding onto the ball.
And with 17 minutes remaining, substitute Higuain all but put the tie to bed by guiding a header into the back of the net from Xabi Alonso’s free-kick into the box.
Ronaldo’s acrobatic attempt at a fourth was blocked by Eboue, who had initially allowed the Portuguese space for the shot, but Mourinho's men had done their job, and played out the remaining minutes in control to set up what looks like a straightforward second leg.