The Los Blancos were imperious at home, cruising to a 4-1 victory as Bernardo Silva, Arda Guler, Kylian Mbappe, and Yan Diomande scored against the visiting Germans, who could not contain their sparkling attack in the closing stanza.
However, Jose Mourinho's men took a while to get into gear. The first clear chance came for Leipzig in the 28th minute, with Romulo Cardoso's shot inside the area forcing Real's gloveman Thibaut Courtois to make a brilliant save. The Belgian stopper was called on again minutes later, making himself big to deny Christopher Nkunku.
Bernardo Silva finally opened the scoring in the 43rd minute. A cut-back pass from Federico Valverde teed up Guler, who forced a save from Maarten Vandevoordt. But Silva was on hand to capitalise on the rebound and break the deadlock.
With the lead secured, halftime arrived. And right after the break, Valverde had a chance to extend the lead with a slightly angled shot inside the area, which Vandevoordt deflected in the 47th minute.
But the Los Blancos faithful didn't have to wait much longer. Jude Bellingham delivered a cross, Mbappe towered over Vandevoordt with a header and a poaching Guler nudged it over the goal line for his second goal in two matches.
Mbappe extended the lead with a spectacular right-footed shot from the edge of the area in the 83rd minute. But the goal of the match came from the dangerous right foot of Diomande, who sealed the rout with a stunning volley into the top corner in the dying embers of the clash.
Despite the comfortable victory, Mourinho has remained on-brand and proved himself a hard-taskmaster.
"No one is where I want them to be," he told the post-match press conference.
"I always want to improve. I've been here for over a hundred days. Obviously, we are not where I want, but there are things we are doing better today than before. If you compare this victory to those against Rayo Vallecano or Malaga, we are improving.
"The goal we conceded I didn't like because I put myself in the goalkeeper's position. Courtois made two incredible saves that kept the game open for us to win. Just as a striker loves scoring goals, a goalkeeper loves going home with a clean sheet. The goal we conceded today and the one against Sevilla came from being overconfident and from someone thinking the game was already won. I don't like that."
Mourinho and Real Madrid now turn their attention to the El Clasico at Barcelona on Sunday.
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