The French striker's two goals, combined with an own-goal by defender Manuel Farrando, proved enough despite late strikes from Nahuel Arroyo and Gonzalo Di Renzo that threatened to spoil Real's evening in front of a raucous crowd.
Mbappe, who came into the game with 56 goals scored in all competitions in 2025, is now just one goal shy of the 59-goal calendar-year record set by Ronaldo in 2013.
With one match still to play this year - on Saturday against struggling Sevilla in LaLiga at Santiago Bernabeu - the French forward could surpass the Portuguese great.