Vinicius put Madrid ahead with a shot into the top corner in the first half and Belgian superstar De Bruyne equalised for the visitors with a powerful first-time shot after the interval.
The second leg will be played next week at Etihad Stadium in Manchester. The first leg of the other semi between Italian rivals Inter Milan and AC Milan is on Wednesday.
"An interesting game. It was difficult for us in all the first half and the second half was much better. We had good control of the game," Madrid boss Carlo Ancelotti told BT Sport.
Madrid beat City in last year's semi-finals and went on to win a record-extending 14th Champions League title while the English club again fell short of European success.
City controlled possession but couldn't translate it into significant scoring opportunities. Erling Haaland wasted a few chances early on Tuesday night but wasn't much of a threat throughout the game at Santiago Bernabeu Stadium.
The Norwegian came into the match having scored 12 of City's 26 goals in the Champions League this season and was five short of Cristiano Ronaldo's single-season record of 17 for Madrid in 2013-14.
Vinicius opened the scoring in the 36th minute with his seventh Champions League goal this season. The Brazil forward picked up a pass by Eduardo Camavinga and used one touch to set up his right-footed shot from outside the area.
City struggled to get close to Madrid's goal but De Bruyne found the net in the 67th with a firm one-timer from outside the area after the home side lost possession because of a poor pass across the field by Camavinga.
"He's (De Bruyne) a massive player for us, always he's been great and he helped us in the moment we most needed it," City midfielder Rodri told BT Sport.
"We were suffering a bit in the second half because they were keeping the ball and, with his goal, it gave us the confidence to keep pushing.
"We knew no matter what happened here, it wasn't going to be the end. We have the second game at home and we will need the people to support us."
Haaland had not yet joined City when they lost 6-5 on aggregate to Madrid in last year's last four tie.
Madrid are making their 11th semi-final appearance in 13 seasons and trying to win a sixth title in 10 years. City played in their first Champions League final two seasons ago, losing to Chelsea.
Madrid won the Copa del Rey title last weekend but are virtually out of contention in La Liga and can fully focus on City. The English champions remain in a tight Premier League title race with Arsenal.
With PA.
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