Mbappe's stellar trio of goals in the fourth, 33rd and 61st minutes in a 3-1 win padded Madrid's lead to 6-3 on aggregate over the 2023 champions in their two-leg knockout playoff.
"This has been the complete performance — attack, defence, with the ball and without the ball, we showed such high levels of quality," Madrid coach Carlo Ancelotti said.
"Almost the perfect night."
Elsewhere on Wednesday, PSV Eindhoven ousted Juventus in the only one of the eight playoffs this week that went to extra time. Defender Ryan Flamingo scored in the 98th minute for a 3-1 win on the night and 4-3 on aggregate.
Paris Saint-Germain thrashed French rivals Brest 7-0, to run up a 10-0 aggregate score, and will play either Liverpool or Barcelona in the round of 16.
In the early game, Borussia Dortmund started with a 3-0 lead at home to Sporting Lisbon and were barely stretched in a 0-0 draw. Sporting's campaign imploded after coach Ruben Amorim left for Manchester United in November.
Mbappe's three goals in the Spanish capital were classy and decisive — watched by another superstar striker from the sidelines. Haaland was not fit to start for an ultimately overmatched City because of a knee injury suffered late in a Premier League game on Saturday.
A first-time lob over City goalkeeper Ederson — who perhaps advanced too far, too soon — was followed by a low shot after leaving defender Josko Gvardiol on the turf.
The third was a powerful left-footer from the edge of the penalty area when he had lured six City players towards him.
"I have always said I didn't come here simply to complete a dream," Mbappe, who never won a Champions League at Monaco and PSG, said.
"I want to play well, I want to mark an era."
A disappointed City boss Pep Guardiola said: "We've had a poor season. When you finish 22nd (in the league phase), it's a sign that you haven't played well.
"Nothing is forever, but we can't deny what this group of players have done, winning six Premier League titles in seven seasons and reaching the quarter-finals, semi-finals and final in this competition. This time we had to play these two matches against a very strong team and they were better than us."
Real Madrid, PSG, PSV and Dortmund join Bayern Munich, Benfica, Club Brugge and Feyenoord, who all advanced on Tuesday, as playoff round winners who will be unseeded teams in Friday's draw. They will host the first-leg games on March 4-5.
The top eight in the 36-team standings three weeks ago — Liverpool, Barcelona, Arsenal, Inter Milan, Atletico Madrid, Bayer Leverkusen, Lille, Aston Villa — skipped the playoffs round and are seeded in the last-16 draw. They host second legs on March 11-12.
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