Asensio netted in the 87th minute from Dani Carvajal’s excellent cross to give Real the advantage heading into the return leg on March 5.
Karim Benzema swept holders Real into the lead in the second half, before Hakim Ziyech scored a deserved equaliser for an energetic Ajax, who created more than enough chances to win comfortably on the night.
They were also denied a first-half opener when Nicolas Tagliafico headed home only for the goal to be chalked off after a VAR check in a Champions League first as Dusan Tadic was judged offside.
Real goalkeeper Thibaut Courtois, whose blushes were spared by the VAR decision after his error led to the disallowed goal, felt the officials got it right.
The home side thought they had profited from a horror error by Courtois, who allowed a Donny van de Beek header to spill from his grasp and Tagliafico nodded the rebound into an empty net.
Yet referee Damir Skomina called for a VAR check and after a number of replays, ruled that Tadic had been standing in an offside position when the goal was scored.
Benzema put Real in front when he netted on the hour-mark, but Ajax got the goal their play deserved with 15 minutes remaining as Ziyech side-footed home after a sweeping move.
Yet Asensio had the final word, scoring at the back post from Carvajal’s cross.
Tottenham’s Jan Vertonghen scores their second goal – Champions League Round of 16 First Leg – Tottenham Hotspur v Borussia Dortmund – Wembley Stadium, London, Britain – February 13, 2019. (Photo: Action Images via Reuters)
The same day, defender Jan Vertonghen scored once and set up another goal for Son Heung-min as Tottenham Hotspur thumped Borussia Dortmund 3-0 at Wembley Stadium to give them the clear edge following the first leg of their last 16 Champions League tie.
Tottenham looked unfazed by the absence of injured captain Harry Kane and Dele Alli, scoring all three goals in a strong second half to take control of the tie and leave the Germans on the brink of a European exit.
Belgian Vertonghen notched his first goal in the Champions League with a well-timed volley in the 83rd minute after he had set up forward Son for a 47th minute lead. Substitute Fernando Llorente grabbed their third in the 86th, two minutes after coming on.
Bundesliga leaders Dortmund, eliminated from the German Cup last week, were nowhere to be seen in the second half, with speedy teenager Jadon Sancho given no space to operate after the break. The return leg is on March 5.