Jose Mourinho's men hit the Eredivisie champions on the counterattack twice in the first half before putting the match to bed in the second period
Cristiano Ronaldo broke the deadlock midway 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 45. Karim Benzema then added a third minutes after the break to put the match to bed.
Ajax started the game with attacking intentions and came close to opening the scoring within two minutes. Derk Boerrigter tried his luck with a low shot from the edge of the area after a good cross from the right, but Iker Casillas showed his class as he kept the ball out with a fine reflex save.
The Spain international was again called into action shortly after when Siem de Jong popped up in the Madrid area and Casillas again was up to the task.
The hosts then took over the initiative and should have grabbed the lead in the 17th minute. Sami Khedira set up Karim Benzema in front of an empty goal, but the France international miraculously aimed wide from 10 yards out. Cristiano Ronaldo then came close after a good pass from Ricardo Carvalho, but Ajax goalkeeper Kenneth Vermeer made a superb save.
Nevertheless, the Ajax No. 1 didn't have an answer to Ronaldo's shot midway through the first half as the Portugal international fired home from inside the area 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 the Bernabeu and Kaka doubled the home side's lead shortly before the interval with a shot into the far corner.
Real Madrid continued to press after the break and another superb counter resulted in their 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 to Kaka, who gave Benzema an unmissable chance and the Frenchman tapped home from five yards out.
Ajax didn't give up though and De Jong, Thulani Serero and Christian Eriksen all tried their luck from long range. However, they failed to trouble Casillas and the Amsterdam giants were lucky not to concede a fourth goal when Kaka placed his shot wide after a quick counterattack.
The biggest chance for the Eredivisie titans came Vertonghen's way in the closing stages of the match, but the Belgium international's header from close range was punched away for a corner by the Madrid glovesman.
Madrid have now collected six points from two games and top Group D. They host Olympique Lyonnais on October 18 in their third game of the group stage.
Ajax sit third in the section with only one point from their opening two games. Their next Champions League match is the away clash versus Dinamo Zagreb in three weeks.