Los Blancos came to the game on a high after beating Atletico Madrid 3-1 in LaLiga on Saturday, while Ajax slipped to a 1-0 defeat against Heracles in the Eredivisie over the weekend.
The match got off to a lively start with attacks from both ends although Vinicius Junior caught the eye with his pace and nearly opened the scoring in the 15th minute with a curling strike that was tipped over the bar by Ajax goalkeeper Andre Onana.
Dusan Tadic almost broke the deadlock for the hosts in the 27th minute with a swerving strike, but his effort came off the woodwork with Thibaut Courtois well beaten.
Nicolas Tagliafico had the ball in the back of the net for Ajax with a header inside the box seven minutes before the break but the goal was disallowed as the Video Assistant Referee (VAR) spotted an offside leading up to the goal.
The visitors were on the back foot in the early exchanges of the second stanza but they showed their quality on the hour-mark as Karim Benzema broke the deadlock with a clinical finish inside the box after being teed up by Vinicius Junior.
Ajax finally got on the scoresheet as the lively Hakim Ziyech equalised 15 minutes before time with a close range finish after a good attacking move, 1-1.
Los Blancos went in search for the winner and they found it three minutes before time through Asensio who punished the hosts with a finish at the back post following a counter-attack.