Mbappé sent a right-footed shot into the upper corner 10 minutes into Sunday's match for his fourth goal in as many games with Madrid in all competitions. It was Mbappé's sixth goal in his last eight matches with Madrid.
He struggled early on with his new club, and Mbappé said his lowest point came when he missed a penalty kick in the team's 2-1 league loss at Athletic Bilbao on December 4.
"I know I have a lot more to give," Mbappé said on Sunday. "The last few games I've played better, I took a lot of positives from the Bilbao game, when I hit rock bottom."
The France star said that made him realise "I have to give my all for this jersey and play with personality."
"The settling-in period is over, as the coach says. I feel very comfortable in the team and I play better with the others on the field. The team is playing much better."
Federico Valverde, Rodrygo and Brahim Díaz also scored in the comfortable home victory that allowed Madrid to finish the year one point behind Spanish league leaders Atletico Madrid.
Atletico rallied to shock Barcelona 2-1 on Saturday with a stoppage-time goal by Alexander Sorloth. Third-place Barcelona are two points behind Madrid, having played an extra game.
Valverde scored in the 20th and Rodrygo in the 34th before Sevilla got on the board with Isaac Romero in the 35th. Díaz extended Madrid's lead in the 53rd and Dodi Lukebakio got the visitors' other goal in the 85th at the Santiago Bernabeu Stadium.
It was the last game for Sevilla and Spain great Jesús Navas, who is officially retiring at the end of the year. The defender was honoured by Sevilla and Madrid players and fans.
Substitute Navas came on midway through the second half.
"What happened today was spectacular," the 39-year-old Navas said, unable to hold back tears. "I had never seen anything like it in my life on a rival field. It was crazy."
Navas helped Sevilla win four Europa League titles and Spain clinch the 2010 World Cup and the 2012 and 2024 European Championships. He was with Manchester City when it won the 2014 Premier League.
Second-to-last Valencia salvaged a 2-2 home draw with Alaves, thanks to a goal by Dani Gómez eight minutes into second-half stoppage time after the visitors had taken the lead with Joan Jordán in the 88th.
Thierno Barry scored a hat trick and Gerard Moreno and Pau Cabanes added one goal each as fifth-place Villarreal won 5-2 at Leganes, while Las Palmas won 1-0 against 18th-place Espanyol. Ninth-place Real Betis were held by 12th-place Rayo Vallecano to a 1-1 draw at home.
