The Santiago Bernabeu side hit the Eredivisie champions on the counter-attack twice before the break and held on to its lead with ease in the second half
Cristiano Ronaldo broke the deadlock halfway through the first half after a good start from the Dutch champions, before Kaka doubled Madrid's lead in the closing stages of the first half. Karim Benzema then added a third minutes after the break to put the match to bed.
The hosts took the initiative early on and were ahead through Ronaldo's shot halfway through the first half after a brilliant attack. Mesut Ozil started the counter inside his own half and set up Ronaldo, who reached Kaka. After a good pass from the Brazilian, again Ozil and finally Benzema, the ball ended up in the feet of Ronaldo once more and he found the net with a low shot.
The opener pretty much ended Ajax's ambitions of getting a good result at Santiago Bernabeu and Kaka doubled Madrid's lead shortly before the interval with a low shot in the far corner.
Real Madrid continued to be the more dangerous side of the two after the break without really dominating possession, and yet another superb counter resulted in its third goal in the 49th minute. Xabi Alonso found Alvaro Arbeloa with a brilliant long pass down the left and the full-back squared it off to Kaka, who gave Benzema an unmissable chance and the Frenchman tapped home from five yards out.
Ajax didn't give up though after conceding a third goal and De Jong, Thulani Serero and Christian Eriksen all tried their luck from long range. However, they either failed to trouble Casillas or aimed wide and the Amsterdam giants were lucky to escape a fourth goal when Kaka placed his shot wide after a quick counter attack.
Real Madrid has now collected six points from two games and sits atop of the table in Group D. It hosts Olympique Lyonnais on Oct. 18 in its third game of the group stage.
Ajax sits last in Group D with only one point from its opening two games. Its next Champions League match is the away clash versus Dinamo Zagreb in three weeks time.