The 22-year-old opened the scoring after 14 minutes, skipping past Real goalkeeper Thibaut Courtois and firing the ball between two defenders on the goal line.
Chelsea should have opened up a commanding lead after dominating the early exchanges, but profligacy in front of goal allowed Real a route back into the game.
Karim Benzema fired a long-range warning shot off the post, before eventually drawing the host level with a wonderful touch to control the ball on his head and then drilling it into the roof of the net.
It was the Frenchman’s 71st goal in the Champions League, moving him up to fourth on the all-time goalscoring list alongside legendary Real striker Raul.
Benzema is just two behind Robert Lewandowski in third, with the Pole unable to add to his tally this season following Bayern Munich’s quarterfinal defeat to Paris Saint-Germain.
Chelsea boss Thomas Tuchel will have certainly left Madrid with the feeling that Tuesday night was a missed opportunity. For the neutral, next week’s second leg is tantalizingly poised but Chelsea’s German coach will likely feel his side should have one foot in the final.
Forward Timo Werner’s wretched form in front of goal continued — he’s averaging a goal every four games this season — with the German hitting the ball straight at Courtois when completely unmarked just six yards out.
Real Madrid did eventually get a foothold in the game and closed out the match in the ascendancy, with Toni Kroos’ deflected effort skidding just wide and Raphael Varane’s header hitting Ben Chilwell and flashing across goal.
Chelsea’s players will no doubt still be kicking themselves, knowing its not often Zinedine Zidane’s side is caught cold in the Champions League.
“We started the game very well, with a lot of courage and quality,” Tuchel told BT Sport after the match. “We deserved to win the first half, we had chances. Unfortunately, they scored from a set-piece and they had nothing else, we didn’t allow any chances.
“The goal was well deserved and we should have scored at least one more. We conceded more or less out of nothing and that can always happen against individual quality.
“It was a disappointing score at halftime. We had to stay calm and not lose confidence. The second half was very tactical, you could feel that we are a bit tired. We only had a few days to recover from another tough away game. We have to live with 1-1.”