Real were left with 10 men before halftime when Mbappe saw a straight red after taking down Alaves midfielder Antonio Blanco as the referee overturned his initial decision of booking him with a yellow after consulting with VAR.
Real Madrid moved four points clear of Barcelona at the top of La Liga with Cristiano Ronaldo scoring either side of a Gareth Bale strike in a 3-0 win at Getafe on Sunday.
Dramatic finale as Valencia denied by 10-man Levante
Real Madrid ensured top spot in La Liga at the midway point of the season when Cristiano Ronaldo struck twice in a 3-0 win at Getafe on Sunday before Lionel Messi's hat-trick helped Barcelona to a 4-0 victory at Deportivo La Coruna.
Lionel Messi scored twice as Barcelona crushed Getafe 5-2 on Thursday to stay in the hunt for the La Liga title.
The victory takes Barcelona up to fourth with 10 points after six games, one point behind surprise leaders Granada, Athletic Bilbao, who visit Leganes on Wednesday, and Real Madrid ahead of their game at home to Osasuna the same night.
Champions Real Madrid were beaten at home by promoted Cadiz, while Barcelona fell to their first defeat in La Liga under new coach Ronald Koeman as they lost to Getafe.
An off-key Liverpool were frustrated for a second successive game by struggling opponents as they were held to a 0-0 Premier League draw at Newcastle United on Wednesday.
Having headed into the match tied on 47 league goals with West Ham's former stalwart Paolo Di Canio, Antonio was delighted to have surpassed the Italian as he celebrated by lifting a cardboard cut-out of himself at the side of the pitch.
Real Madrid extended their unbeaten run to 25 matches and rejoined Barcelona and Atletico Madrid at the top of La Liga when Jese, Karim Benzema and Luka Modric scored in a 3-0 win at Getafe on Sunday.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
Griezmann special earns Atletico 1-1 draw at Sevilla
News of all that's transpired on and off the football field
Real Madrid midfielder Luka Modric is set to miss the rest of the year with a thigh injury, the La Liga leaders said in a statement on Monday.