Portugal forward Cristiano Ronaldo opened the scoring in the 25th minute at the Bernabeu, finishing off a sweeping breakaway move. Brazil playmaker Kaka and France striker Karim Benzema then struck either side of half-time.
"It was a good win and puts us in a good position in the group," Kaka told Spanish television.
"We need to continue like this and I think we can seal the group very soon," added the 29-year-old who was given a rousing ovation when he was substituted in the 75th minute.
Kaka joined Real from AC Milan at the end of the 2008/09 season for a fee of almost 70 million euros but a series of injuries have prevented him rediscovering the form that won him the World Player of the Year award in 2007.
He looked back to his sparkling best on Tuesday as Real, who were knocked out by bitter rivals and eventual champions Barcelona in last year's semi-finals, strengthened their hold on top spot with six points from two matches.
Olympique Lyon have four points thanks to their 2-0 win at home to Dinamo Zagreb, with Ajax on one point in third and the Croatian team bottom on zero.
Real coach Jose Mourinho, serving the final game of a three-match ban, opted for an attacking formation against the Dutch side with Kaka and Germany playmaker Mesut Ozil operating just behind Ronaldo and Benzema.
However, it was Ajax who started brightest and Iker Casillas had to make a smart save low to his left from Christian Eriksen's snap shot in the first minute.
Casillas was called into action again in the 15th when Kolbeinn Sigthorsson burst through the centre and the Spain keeper blocked the Icelander's shot.
Real's first real chance came two minutes later when Sami Khedira found space on the right and pulled the ball back for Benzema but the Frenchman scuffed his shot wide.
Kenneth Vermeer in Ajax's goal did well to sprint off his line and block a Ronaldo effort in the 22nd but was powerless to prevent the forward giving his side the lead three minutes later.
Ronaldo, another former World Player of the Year and the world's most expensive footballer, smashed the ball into the net after a rapid passing move involving Ozil, Kaka and Benzema.
Kaka was allowed too much space on the edge of the area and fired a powerful left-foot drive into the corner in the 41st minute and any hopes of a second-half Ajax revival were snuffed out in the 49th when Benzema sidefooted home Kaka's pass.
Ajax coach Frank de Boer, who helped the club win the European Cup in 1995 before making more than 150 appearances for Barcelona, said his side needed to be "smarter and better organised" if they were to challenge teams like Real.
"I said in my talk before the game that Real Madrid were very dangerous on the break and they showed that again tonight," the former Dutch international said.
"We started pretty well though and that should give us some confidence for the coming games.
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