After Atletico Madrid beat Barca on Saturday to claim top spot at Christmas, Carlo Ancelotti's side also took advantage with a comfortable home win which leaves them a point behind the leaders.
Madrid coach Ancelotti said ahead of Sevilla's visit that Mbappe's adaptation period had ended following his summer switch from Paris Saint-Germain and the French forward proved the coach right with a strong performance and his 14th goal of the season across all competitions.
Fede Valverde also netted a brilliant effort from range, with Rodrygo Goes and Brahim Diaz on the scoresheet for the hosts too.
Isaac Romero and Dodi Lukebakio scored for Sevilla, although they were thoroughly outplayed on veteran defender Jesus Navas' final game for the club.
"I think that we know each other better, my arrival changed a lot of things, and now, as the coach said, the adaptation is over and I feel very good in the team," Mbappe told Real Madrid TV.
"We can see on the pitch that I click better with my team-mates and now we're all playing better."
Mbappe, back after a brief absence with a thigh injury, scored for Madrid in midweek as they won the Intercontinental Cup.
It was welcome relief for the forward after missing two penalties in recent weeks against Liverpool and Athletic Bilbao, as well as suffering criticism for his form.
"I know I've got much more in my legs than I'm showing, but in the last games I've played better," Mbappe added.
"The Bilbao game was good for me, I hit the bottom, I missed a penalty and it was a moment to realise that I have to give everything for this shirt and show my personality."
With Vinicius Junior suspended, Mbappe took the reins and broke the deadlock in the 10th minute as Madrid brought the ball out from the back and worked it to Rodrygo on the left flank.
The Brazilian squared to Mbappe on the edge of the area, who took one touch to control, another to set himself and with his third, smashed a fierce effort past the helpless Alvaro Fernandez.
Madrid's second, 10 minutes later, was even better, with Valverde firing a screamer into the top corner from over 30 yards out after a short corner routine.
Ancelotti's side were in full flow and the third followed in the 34th minute when Lucas Vazquez crossed for Rodrygo, who finished with aplomb.
Navas bows out
Sevilla hit back within a minute, with Romero nodding home from Juanlu Sanchez's cross after good work by Dodi Lukebakio.
Sevilla came out strongly in the second half and Romero should have added a second but fired straight at Thibaut Courtois when well placed.
Instead it was Madrid who stretched their lead, with Mbappe dinking a superb pass through for Diaz to finish clinically.
Sevilla brought on Navas after the hour mark and he was applauded by the Santiago Bernabeu, with this his 705th and final appearance for the club, far more than any other player.
Madrid and Sevilla players together gave the retiring Spanish great -- a World Cup winner in 2010 and two-time Euros champion -- a guard of honour at the start of the game.
Navas, 39, won four Europa Leagues and two Copa del Rey trophies with Sevilla, but his final appearance ended in disappointment for the Andalusians, who were outplayed in the Spanish capital.
Fernandez saved from Rodrygo after Mbappe rounded the goalkeeper and passed the ball back to his Brazilian strike-partner, as Madrid looked for a fifth.
Lukebakio pulled one back late on for Sevilla as Madrid were able to finish an impressive year, in which they became Spanish and European champions, with a good result.
