Eden Hazard has said Maurizio Sarri's style of play is "more like my philosophy of football" as the Chelsea coach attempts to turn the club's faltering season around. "He did everything he had to do from the moment he came into the pitch".
However, the defending champions secured the winning goal with four minutes remaining in the half, with substitute Marco Asensio finishing off a superb cross from Carvajal.
Real Madrid have been in superb form in recent weeks but they are still behind FC Barcelona in the La Liga table, trailing the leaders by six points after 23 games.
I'm just happy to be working with Maurizio again at a big club like Chelsea which has so much history and wonderful team-mates.
"They are the future of Real Madrid", Solari said.
Tagliafico's header shortly before half time was chalked off when, after re-watching the incident as part of a VAR review, referee Skomina deemed Dusan Tadic to have been interfering with play from an offside position.
Ten Hag was not convinced by the video images he saw.
Hazard has postponed contract talks in order to keep his summer options open, and last month Sarri said he should join Madrid at the end of the season if he believes that will make him happy.
"His adaptation has been very fast", Solari said.
Ajax got the goal their play deserved with 15 minutes remaining as Ziyech side-footed home after a sweeping move, latching on to a delivery from David Neres on the left.
Tadic then held off Sergio Ramos to fire in a shot that hit the post, and Ziyech missed another one-on-one chance with Courtois as Ajax's incisive passing stretched the visitors.
Despite being a defender by trade, Ramos is most revered in the Spanish capital for his dramatic last-gasp headed equaliser against city rivals Atletico in the 2014 Champions League final.
Young forward Vinicius Junior is will start alongside Bale and Karim Benzema in a front three.
Ajax claimed a foul in the build-up to the goal, but this time the VAR did not intervene and Real will take a slender advantage back to Madrid.