Real, chasing a 15th European Cup, levelled in the 83rd with Vinicius's penalty, after Rodrygo was felled by a clumsy challenge from Kim Min-jae, to set up a mouth-watering return leg in Madrid next week.
Real Madrid's Vinicius Jr scored twice, including a late penalty, to snatch a 2-2 draw at Bayern Munich in an entertaining Champions League semi-final, first leg on Tuesday, leaving the tie wide open.
The Brazilian, who put Real in front after 24 minutes, has now scored in the semi-finals for a third successive season.
Bayern, with only the Champions League title left to fight for, had scored twice in four minutes early in the second half through a Leroy Sane strike and Harry Kane penalty to turn the game around before Vinicius' spot kick.
"We always want to win but we know that this competition is like that, you can't give away balls because teams score the chances they have," Vinicius Jr said.
"We have to keep our heads calm, rest until next week and we know that we and the fans are going to leave everything at the Santiago Bernabeu to qualify."
"Now it's time for a magical night at home to win and secure our place in the final," he added.
Facing each other for a record eighth time at this stage of the competition, it was Bayern who got off to a strong start, racking up half a dozen attempts on goal by the 15th minute with Sane and Kane coming close.
Real needed only one chance to score though, stunning the home crowd against the run of play when Kroos sliced open the Bayern defence with a through ball and Vinicius Jr chased it down to beat goalkeeper Manuel Neuer.
Kroos almost added another himself in the 51st but his curled shot was palmed wide by Neuer. Instead, it was Bayern who scored two minutes later with a solo effort and shot from Sane that eluded goalkeeper Andriy Lunin for a deserved equaliser.
Their comeback was complete in the 57th when Jamal Musiala was brought down in the area by Lucas Vazquez and Kane sent Lunin the wrong way from the spot to put the home side ahead.
Real, chasing a 15th European Cup, levelled in the 83rd with Vinicius's penalty, after Rodrygo was felled by a clumsy challenge from Kim Min-jae, to set up a mouth-watering return leg in Madrid next week.
"Everything we're fighting for is in this competition," said Kane. "We've just got to find a way to get it done. Real Madrid away is going to be tough but we've got to go there with full belief and go for the win.
"The Champions League is the biggest of them all. If we can somehow get our hands on it, it will be an amazing season – but there's still a long way to go."
The winners will face either Borussia Dortmund or Paris St Germain, who meet in the second semi-final on Wednesday.
