Arda Guler fired Los Blancos ahead on the half-hour mark, drilling the ball into the top corner from the edge of the area.
France forward Mbappe doubled the lead in the 37th minute with a sublime show of footwork.
Jude Bellingham flicked on a pass from the left to the edge of the penalty area, where Mbappe took the ball in his stride, spinning clear of his marker before holding off another defender and then side-stepping the goalkeeper to slot home.
Mbappe scored his second of the night in the 63rd minute, clipping a Panenka penalty over Sevilla goalkeeper Odysseas Vlachodimos.
Manu Bueno pulled a goal back for Sevilla with 10 minutes left, but Yan Diomande then fired in Real Madrid's fourth.
Real Sociedad are fifth after a 5-2 win at bottom side Malaga, with Mikel Oyarzabal scoring twice.
In Italy, Lazio moved to second in Serie A with a 3-0 win at Juventus.
Oliver Provstgaard headed Lazio in front shortly before the break and Gustav Isaksen drilled in a second after 66 minutes.
Substitute Fisayo Dele-Bashiru added a late third, leaving Gennaro Gattuso's side level with leaders Inter Milan on 19 points.
AC Milan held off a fightback from Atalanta to close out a 3-2 win at San Siro and move up into fourth.
Lyon are top of Ligue 1 in France after coming from behind and finishing with 10 men as they beat Nice 2-1, but only after the visitors saw a stoppage-time equaliser ruled out.
Lassine Sinayoko's penalty deep into added time gave Paris FC a dramatic 4-3 win over Rennes. Esteban Lepau had scored a hat-trick of spot-kicks for the visitors, with his third coming in the 88th minute.
Monaco dropped to fifth after losing 1-0 at Lorient.
In the Bundesliga, Bayer Leverkusen extended their winning run to five games in all competitions after a late goal from Patrik Schick secured a 2-1 victory over top-four rivals Freiburg at the BayArena.
Bottom side Borussia Monchengladbach slumped to a sixth straight defeat after losing 2-1 at home to Hoffenheim.
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