Rafa Mir headed the visitors into an early lead before Karim Benzema levelled with a tap-in.
Vinicius completed Real’s comeback when he cut inside and found the top corner with a brilliant right-footed shot.
It was Real’s sixth win in a row in all competitions.
Carlo Ancelotti’s side were stung into action when Mir planted a header past Thibaut Courtois in the 12th minute.
The hosts hit back through Benzema, who was left with an easy finish after Sevilla goalkeeper Yassine Bounou could only push Eder Militao’s long-range effort onto the post.
After Vinicius’ goal, Courtois made a vital stoppage-time save to keep out Thomas Delaney’s header.
Real are now four points clear of rivals Atletico Madrid, who thumped Cadiz 4-1 earlier on Sunday with Thomas Lemar, Antoine Griezmann, Angel Correa and Matheus Cunha on target for Diego Simeone’s side, and also Real Sociedad.