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The goals for Real Madrid were scored by Frenchman Kylian Mbappé (30') and Brazilian Vinicius Junior (50'), while Alavés' goal came from striker Toni Martínez (90+3').
Real Madrid now have 73 points, six points behind leaders Barcelona, who have 79 and host Celta de Vigo on Wednesday.
In contrast, Alaves' tally remains frozen at 33 points in 17th place, just above the relegation zone, and they may drop further in the standings pending Elche's (32 points) match against Atletico Madrid on Wednesday.