The Spanish champions are top of Group D after the win and look likely to qualify for the Champions League knockout stages, while Ajax are struggling in the competition following their second defeat in the competition.
Sports Mole takes a look at the key talking points from tonight's match in the Dutch capital.
On Target: 1
Yellow Cards: 0
Red Cards: 0
On Target: 12
Yellow Cards: 1
Red Cards: 0
Was the result fair?
In truth, the result probably was a fair reflection of the match. Madrid completely dominated the first half and despite a good period of play for Ajax midway through the second period, the Spanish champions had more than enough chances to justify the scoreline.
Frank de Boer will be disappointed with his side's display tonight. The hosts needed to dictate the tempo of the match and they failed to do so in the first half. Ajax's key players didn't perform with Christian Eriksen having virtually no impact on the game.
It was a very good away performance from Los Blancos. Jose Mourinho will be delighted that he could rotate his players and still record such an emphatic victory. Despite 10 minutes of poor defensive work in the second period, Madrid dominated proceedings throughout.
Jonas Eriksson didn't have a busy tonight in Amsterdam. There were very few big decisions to make and he was only forced to show the yellow card on one occasion, to Michael Essien.
Sports Mole's man of the match
Who else could it be? Cristiano Ronaldo was at his best for Madrid with a fantastic hat-trick to take the game away from Ajax. If his first goal was an easy finish, he deserves credit for his sublime second-half brace.
It's difficult to criticise De Boer's selection with little else in reserve for the Dutch club but Ryan Babel was poor as the lone striker. The former Liverpool forward was non-existent for long periods of the match and Ajax desperately missed an attacking threat.
Ajax: De Boer's men continue their search for a first point in the competition this season by welcoming Manchester City to the Amsterdam ArenA. A third defeat must be avoided by the hosts.
Real Madrid: Mourinho takes his men to Germany on October 24 and a victory against Borussia Dortmund could all but confirm qualification for the Spanish club. However, after an impressive display against Man City on Wednesday night, Dortmund will fancy their chances of causing an upset.