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The home side should have taken the lead with only four minutes on the clock. Gareth Bale was released through on goal, but after advancing into the penalty area, he curled his shot wide.
After that, Madrid continued to have the majority of the play, but they failed to fashion another clear opening.
With 20 minutes gone, Carlo Ancelotti's men had had a huge 65% of the possession, while Galatasaray's one attempt had flown high over the bar.
Felipe Melo gave away a free kick 30 yards from goal, which Bale gratefully placed into the corner of the net.
Los Blancos needed only five minutes of the second half to restore their advantage. Angel di Maria teased the away defence down the left before sliding the ball into the box for Alvaro Arbeloa to score from six yards.
Arbeloa missed a chance for his second, but the home fans didn't have long to wait for the next goal. Isco and Arbeloa linked up well and fed the ball to Di Maria, who found the back of the net from 12 yards.
Isco then wrapped up victory and qualification to the knockout stages with the fourth of the night. The Spaniard brought down a high ball, before advancing past a defender. His attempted shot was blocked, but he regained possession and rolled the ball in.