With the score tied in the 38th minute, Nicolas Tagliafico appeared to fire Ajax into the lead by pushing home a rebound following a corner kick.
The goal, however, was ruled out by VAR as it was determined that Dusan Tadic had interfered with Courtois from an offside position.
Many found the call to be a controversial one, but Courtois insists the decision was the correct one.
"The correct decision? I think so. When it happened I thought it could be offside. When the guy headed it I wanted to go and catch it," Courtois said after the win.
"Because of his [Tadic's] intention I made a quick movement. Luckily for VAR, because nobody would have seen it."
Madrid went on to take the lead in the 60th minute on a goal from Karim Benzema, who became only the fourth player to score at least 60 goals in the Champions League alongside Cristiano Ronaldo, Lionel Messi and Raul.
Hakim Ziyech pulled Ajax back with a goal of his own in the 75th minute, tying the match at one apiece in Amsterdam.
But the visitors would take the lead for good in the 87th minute through Marco Asensio, ensuring the three-time defending champions will hold a big advantage as the tie heads to Madrid.
With the win, Real Madrid have now won more Champions League games against Ajax, seven, than any other team in history. They've also scored 22 total goals against the Dutch side, more than any other team.
The two teams will meet once again in Madrid on March for the second leg of their round of 16 tie.