Karim Benzema swept holders Real into the lead in the second half, before Hakim Ziyech scored a deserved equaliser as an energetic Ajax created more than enough chances to win comfortably on the night.
They were also denied a first-half opener when Nicolas Tagliafico headed home but for the first time in Champions League history, the goal was ruled out after Slovenian referee Damir Skomina checked with the VAR and Dusan Tadic was judged offside.
The return leg will be played in Madrid on March 5 when Ajax will seek to reach the Champions League quarter-finals for the first time in 16 years, while Real have not lost a tie at this stage in almost a decade.