Los Blancos lost 1-0 away at Real Betis ahead of welcoming Jose Mourinho's former team to the Estado Bernabeu, in a defeat which ended their 100% league record under the returning Portuguese boss.
However, they were quick off the mark against the defending Serie A champions, as early goals from Kylian Mbappe and Federico Valverde proved enough to seal three European points.
Mourinho was forced to make two starting changes - with Eduardo Camavinga and Arda Guler both suspended - as Trent Alexander-Arnold and Brahim Diaz started in midfield.
Record signing Yan Diomande once again came off the bench, as Mourinho resisted calls to start the Ivorian, and the veteran coach called for patience on the 19-year-old's progress.
"Yan Diomande? We have to go step by step with him.
"He arrived in the last days of preseason, without any training sessions… so we must go step by step with him."
Up next for Real Madrid and Mourinho is a home LaLiga clash with Rayo Vallecano on September 12th.