Garcia, 21, put Madrid ahead from close range early on a hot afternoon at the MetLife Stadium just outside New York City, and Fran Garcia then doubled their lead before the midway point in the first half.
Dortmund never seriously threatened a comeback before a remarkable late flurry of activity, with Maximilian Beier pulling one back in the 93rd minute and Mbappe getting Madrid’s third with a stunning overhead kick.
Serhou Guirassy then completed the scoring with a penalty after Real’s Dean Huijsen was sent off, before the full-time whistle finally blew.
Xabi Alonso’s side find themselves in the semi-finals despite Mbappe still not having started a game at the tournament.
The France superstar, who did not play at all during the group stage due to illness, will now hope to start for the first time when Real take on his old club in a fascinating last-four showdown at the same venue on Wednesday.
Whoever emerges victorious from that tie will be the favourites to go on and win the inaugural edition of FIFA’s expanded competition, with Chelsea taking on Fluminense in the other semi-final.
This match, watched by a near sell-out crowd of 76,611, was a repeat of the 2024 UEFA Champions League final which Real won 2-0.
But while they needed two late goals to claim victory then, this time they seemed to have got the job done early after Alonso sprang something of a surprise with his tactical line-up.
The new Real coach had deployed a three-man central defence in previous games at the tournament, but this time he went with an orthodox back four as Aurelien Tchouameni stepped up into midfield.
Julian Brandt was not far away from giving the German side the lead, but instead it was Real who went in front in the 10th minute.
Garcia had scored three times in Madrid’s first four matches at the Club World Cup, including the winner against Juventus in the last 16.
He stole in between two defenders to meet an Arda Guler cross at the near post and make it 1-0 to the delight of the vast majority of the crowd.
The summer heat contributed to the slow pace of the contest, but Real also effectively killed off Dortmund’s hopes by scoring again in the 20th minute.
Patient build-up play on the right involving the imperious Jude Bellingham and Gonzalo ended with the two full-backs combining as a low Trent Alexander-Arnold cutback was swept in by Fran Garcia.
They should have scored more goals before half-time, with Bellingham — deprived of the chance to face his brother Jobe who was suspended — firing just wide after a nice dummy by Vinicius Junior.
The latter sent a shot wide when he tried to surprise Gregor Kobel from the edge of the box, while Tchouameni cracked an effort off the frame of the goal just past the hour mark, albeit there was an offside earlier in the move.
Dortmund could have made a real comeback attempt had half-time substitute Beier scored at the other end just before that, although their hopes were briefly raised late on.
Beier did make it 2-1 three minutes into time added on as he controlled a poor clearance and fired a low shot past Thibaut Courtois.
Mbappe, who had come on for Bellingham midway through the second half, then scored his 44th club goal since the start of the season with an overhead effort at the back post from a Guler cross.
Then Guirassy was brought down at the other end, leading to centre-back Huijsen being sent off. Guirassy scored the penalty to make it 3-2 with his 38th of the season and fourth of the competition. (AFP)