The France international bagged three goals to take him past 100 goals for the Spanish giants after joining the club as a free agent in 2024 following his contract expiry with Paris Saint-Germain.
Portuguese coach Jose Mourinho has praised the Frenchman following his match-winning exploits in their first home game of the season at the Santiago Bernabeu on Wednesday.
"I don't like comparing players, but this guy is incredible," said Mourinho to reporters after the match.
"I'm really happy that he made history in the World Cup because there are 25 world champion players, but only one is eternal in football: the player who has the most goals in the World Cup.
"He's made that history, but I see him with a lot of hunger to make history with Real Madrid."
The 63-year-old head coach also emphasized Mbappe's overall ability and contribution beyond his goal scoring threat.
"I always say that with these players, you have to teach them to play as a team and teach them very little from an individual perspective. And when the team struggles to build play, Kylian has tremendous quality," added Mourinho.
"He's not just a goal scorer or the typical forward waiting for the team's offensive play to score. When he drops back to start the play, then combines with Jude [Bellingham], he's already facing goal. He has so much quality, and so do all of them.
Los Blancos turn their attention to Sunday's clash at home to Malaga.