Bayern dominated at the Allianz Arena, showing not only why they won the Bundesliga title this year in record time, but why they are one of the most feared sides in European football.
Barca will have to make history next Wednesday to deny them a place at Wembley on May 25, but with 90 minutes still to be played, the last word in the tie has not yet been spoken.
"I am not a dreamer so I'm not going to dream either," said Thomas Muller, whose brace put Bayern in the driving seat.
"Let's say that we did not expect to win 4-0, but we ran so much and created so many chances that of course it's a great result.
"But you can never tell what will happen in the second leg. I think their pitch is a bit bigger so they will make us run a bit more, but 4-0 is a fantastic result.
"A lot can happen on one night so we have got to remain alert, but our morale is high."
In 11 months since going down to Chelsea in the final at the Allianz Arena, Bayern have transformed into a side who, after sending the records tumbling in the Bundesliga, are now making waves in Europe.
That bitter defeat and three trophyless years have inspired them according to goalkeeper Manuel Neuer and few would now bet against them completing an historic treble this season.
"We are a united team and have lots of quality," said Germany's number one. "The defeats last season have pulled us together and we've shown that in the last weeks and months.
"We can enjoy the night, but we've still got to be careful. We know that in the Nou Camp, Barcelona have played some great games."
The question has got to be asked what, if anything, he will be able to improve in a side who are looking increasingly likely to complete a historic treble this season.
"We have been playing some extraordinary football all season," said Heynckes.
"We have a fantastic team and missing out on success in the past two years has just made us hungrier to win this year.
"This game was a perfect example of that."
It is going to take something more than a great game for the Blaugrana to overturn a four-goal deficit, especially considering the manner in which Bayern tore Barca apart.
However, until the final whistle next Wednesday seals their fate, Barca will carry on believing.
"We've got 90 minutes and we've got to give it a try," said Dani Alves.
"When you play against an opponent who play better than you, then things like this can happen, and we've got to congratulate them.
"Today [Tuesday] Bayern were stronger than us and we've got to take our hats off to them, but there are still 90 minutes to play.
"We still have a second leg and we've got to believe in it, but there's nothing abnormal about what happened tonight [Tuesday]."
After overturning a 2-0 defeat to AC Milan in the last 16, Barca are not giving up the ghost just yet.
"We are Barca and we've got to try to get to the final," said midfielder Xavi Hernandez.
"We need to play a great game, but we know at the same time that it's practically impossible."
Xavi paid tribute to a Bayern side who outplayed and outmuscled the 2009 and 2011 Champions League winners like very few have achieved over the past six seasons.
"They were quicker than us and it was like a siege," he said. "We expected it to be like this.
"They are very strong physically and they were better than us.
"When you make mistakes in the Champions League, you pay the price.
"They were stronger than us. I don't know why we didn't attack well.
"They have extraordinary players like Robben and they just found it too easy to get past us."
The example was not lost on Barca's assistant coach Jordi Roura either.
"They have to be congratulated," he said. "They were superior to us.
"We are in a difficult situation, but we are Barcelona and, as such, we have to make a fight of it in the second leg and try to win.
"We will give it all we've got."