Bernardo Silva opened the scoring for Madrid from close range towards the end of a tight first half, with Arda Guler doubling the record 15-time European champions' advantage soon after the interval.
Real Madrid rout Leipzig to continue perfect European start
Real Madrid claimed a third Champions League victory in as many games by thrashing RB Leipzig 4-1, with Kylian Mbappe and Yan Diomande among the goals for Jose Mourinho's side.
Mbappe bent home a third before Tidiam Gomis pulled one back for the German side and Diomande rammed a volley into the top corner to cap Madrid's triumph late on.
"We know every point is important to get into the top eight, we know we have to win as many games as possible -- we've won three and there are five to go," Mbappe told Movistar.
The French superstar, who hopes to win the Ballon d'Or next week, has netted in each of Madrid's Champions League matches this season and has 12 goals in 12 games.
"I'm doing well (but) I think I can do more," said Mbappe.
"I'm one of the few players who always has to demand more from himself... right now it's a good moment, but we have to keep going and I have to do more."
Their fourth consecutive win across all competitions will boost Madrid's morale ahead of Sunday's La Liga Clasico against bitter rivals Barcelona.
Without a major trophy for two seasons and having endured a shaky domestic start, Madrid can at least boast a perfect European record in the league phase, unlike Barca after their defeat at Paris Saint-Germain on Tuesday.
"For a Clasico, confidence doesn't exist," Mourinho told Movistar.
"It's one more league game, but it's not a game like the others. We're losing 24 hours of rest (compared to Barca)."
Mourinho started with Vinicius, serving a four-match ban in La Liga, on the left flank and benched former Leipzig winger Diomande, despite his encouraging form.
Visitors Leipzig created the first big chance, with Madrid stopper Thibaut Courtois getting down low to make a superb save from Romulo Cardoso.
Vinicius, who improved on a poor showing at Roma last week without breaking out of his rut, drew a save at full stretch from Leipzig's Maarten Vandevoordt.
Madrid carved out an advantage in the final stages of a low-key first half when Valverde cut the ball back for Guler, whose shot was blocked by Vandevoordt, but Silva darted in to score his first goal for the club.
Guler put Madrid two goals ahead in the 52nd minute, holding off a defender and turning home Mbappe's header back across goal from Jude Bellingham's cross.
- Sad Vinicius -
Mourinho sent on Diomande for Vinicius with 20 minutes remaining, with the Brazilian left looking downcast on the bench, aware he cannot play again until November 4, when Madrid visit AEK Athens.
"I think it's good that he's sad, because it means he wants to give a lot to the team, to the fans," said Mbappe.
"I think he just needs to stay calm, he needs to be calm, proud of who he is, because a great player must always be proud of what he is, and keep his confidence, because the quality is there."
Mourinho thought the Brazilian winger had a decent game.
"I don't want to say he's sad, because that's a feeling only he can say if he has, but his coach is happy," said Mourinho.
Vinicius watched on as Madrid's record 140 million euro ($157m) signing Diomande pulled the ball back to Mbappe on the edge of the box for the third, with the France attacker bending home.
Leipzig quickly grabbed a consolation goal at the other end as Dean Huijsen switched off, with Gomis firing past Courtois.
Diomande ended proceedings with a bang as he rattled an emphatic volley from Brahim Diaz's cross into the top corner for his third goal in his last four appearances.
