Asensio, was unmarked at the far post as he tapped in a cross from the right by Dani Cavajal in the 87th minute to put Madrid in a strong position going into the second leg on March 5.
Ajax looked on course for a draw at the Johan Cruyff Arena when Hakim Ziyech shot under Thibaut Courtois in the 75th minute to cancel out Karim Benzema’s opener 15 minutes earlier.
Ajax, a four-time European champion that last won the title in 1995, dominated the first half and looked to have taken the lead only to have the video assistant referee rule out Nicolas Tagliafico’s 37th minute header because Dusan Tadic was offside standing in front of Courtois. It was the first time VAR had been used to disallow a goal in the Champions League.
Kasper Dolberg came close to levelling again in stoppage time, but Courtois stuck out a hand to block his effort.
In the night’s other round-of-16 match, Tottenham beat Dortmund 3-0 at Wembley. In Amsterdam, Benzema struck a powerful shot past Andre Onana on the hour after a strong run from the left by Vinicius Junior to put the 13-time European champion ahead.
Madrid’s lead lasted 15 minutes before David Neres crossed from the left and substitute Dolberg let the ball run to Ziyech, who shot low under Courtois. Ajax, in the last 16 of the Champions League for the first time since 2006, had lost its last six matches against Madrid.