At the Santiago Bernabeu, the European champions had a difficult day until Federico Valverde snapped the tie with 10 minutes remaining.
Real Madrid did not put on a particularly memorable performance, but they still managed to win and earn three more points.
Real Madrid defeated RB Leipzig 2-0 in their Champions League match to maintain their perfect start to the year.
Federico Valverde maintained his calm to bend a left-footed drive home in the 80th minute, giving Los Blancos the lead for the first time.
After receiving a cutback from Toni Kroos, Marco Asensio, who had just entered the game, scored a fantastic goal to seal the victory.
Leipzig had its chances, but they lacked a decisive advantage in the final third and were deservedly penalized by the champions.
After the match, the illustrious Italian coach said he was delighted with his team’s performance because the visitors made things very difficult for them. Ancelotti said to Diario AS.
“Yes, it was the thickest [most viscous] game, to put it like that. It was fantastic game, firstly we did not want them to catch us on the counter and for that reason, we did not move the line forward as much in the first half.
“It was a controlled game at the back and only twice did they get in behind us. We wanted to play the match to win it. Their best asset was the counter-attacks. The central midfielders were very important. In the second half, they lowered their intensity and we took advantage of our fitness. We were intelligent.”
Real Madrid next match will be against Atletico Madrid on Sunday.
RB Leipzig travels to face Borussia Mönchengladbach in the Bundesliga on Saturday.