The club got off to a blistering start, scoring two goals by the 28th minute.
Luka Modric got things started for Madrid, lofting a beautiful ball past the Ajax defense while Karim Benzema cradled the ball and then found Cristiano Ronaldo for the score in the 13th minute.
Modric was once again a pivotal factor in the 28th minute when he placed a lob just past the Ajax defense. Jose Callejon made a couple of nice touches and then sent it into the lower right-hand corner of the net with grace.
Kaka added to the scoring barrage in the 49th minute with a curling, 20-yard beauty into the top of the net after Ronaldo found him with a nice pass.
Ajax showed some life later in the second half when Derk Boerrigter found the net after a mistake by Antonio Adan, swinging the ball past the frustrated goalkeeper.
But it wasn't enough, as the early explosion by Madrid, coupled with yet another goal by Callejon in the 88th minute, proved to be too much to overcome.
Madrid finished second in Group D behind Borussia Dortmund.
Once Modric found Benzema down the pitch, it was only a matter of seconds before Ronaldo would come storming in and slam it home.
While Modric made a picture-perfect pass to Callejon, it wasn't over at that point. Callejon made a beautiful touch past goalkeeper Kenneth Vermeer that just nicked inside the goal post.
Kaka's swinging shot past the defense and into the upper left-hand corner of the net in the 49th minute was simply unstoppable. It was yet another brilliant play by a Madrid player on Tuesday.
Jose Callejon, Real Madrid: A
Callejon scored twice in the match, adding insult to Ajax's injury when he thumped home another goal in the 88th minute. He was fantastic throughout and was one of many Madrid players who stepped up.
Cristiano Ronaldo, Real Madrid: A
Ronaldo got Madrid off to a quick start with an emphatic goal in the 13th minute off a pass from Karim Benzema. The talented striker did just what he's expected to do in that position.
The superstar also made a nice pass to Kaka in the 49th minute, which the Brazilian handled with ease while swinging a curving shot into the top corner of net.
Luka Modric, Real Madrid: A
Modric got the Madrid attack started early, gaining possession in the middle of the pitch and finding Karim Benzema with a beautiful pass before Benzema swung it over to Ronaldo for the goal.
He was also responsible for leading the second attack, lobbing the ball beautifully over the Ajax defense before Jose Callejon adeptly made a few touches and fired into the net.
Madrid scored twice in the first half, and a lot of it had to do with the brilliant play of Modric.
Kaka, Real Madrid: A
Kaka's curving shot in the 49th minute was simply a thing of beauty. It was the goal of the match, and there was nothing the Ajax defense, or goalkeeper Kenneth Vermeer, could do about it.
Derk Boerrigter, Ajax: A
Boerrigter was the sole Ajax player who made a difference on Tuesday, threatening a couple of times before firing home a goal in the 59th minute.
He also sent a twirling free kick past the Madrid defense in the 65th minute, but Adan was perfectly positioned to thwart the challenge.
Christian Eriksen, Ajax: C-
With the way Madrid was rolling, Ajax couldn't afford to waste opportunities. Eriksen wasted an opportunity in the 37th minute when he sent a set piece directly at Madrid's two-man wall. Surely the 20-year-old could have done better than that.
Kenneth Vermeer, Ajax: C
It's hard to pin this on Vermeer. Madrid was simply too good on Tuesday, and the 26-year-old didn't have much of a chance. He did well to save six shots while Madrid constantly applied pressure.
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