The Germans football club has been unbeaten in 2020, winning 24 of their last 25 matches in all competitions and they have not lost a Champions League game all season.
Moussa Dembele scored twice for the French outsiders to seal a 3-1 win that sets up a meeting with Bayern Munich.
Bayern’s stunning start to the standout quarterfinal between the only past champions in the last eight saw Thomas Müller score twice and Ivan Perisic and Serge Gnabry add on in the first half-hour.
Barcelona will have to improve significantly to match Bayern Munich in the quarter-finals, who are arguably favourites to win the tournament.
Munich, which had already won its eighth straight Bundesliga title, retained the cup with goals from David Alaba, Serge Gnabry and two from Robert Lewandowski.
With no fans in the stands on a wet night in Bremen, it was a subdued and strange celebration for Bayern’s players, who put on commemorative T-shirts and paid tribute to their absent supporters with cheers.
Thirteen-time winners Real Madrid were drawn against English champions Manchester City while title-holders Liverpool must face Diego Simeone's Atletico Madrid in the Champions League round of 16 following Monday's draw.
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After the last-16 first leg ended goalless at Anfield, five-times European champions Liverpool took control in Munich, bossing the game to become the fourth English team into the last eight
The UEFA Champions League round of 16 will see three England-Germany clashes and a true test of the Premier League v Bundesliga.
Jupp Heynckes takes charge of Bayern for the final time in the German Cup final against Eintracht Frankfurt and has told the club not to call on him again. He is retired.
The first leg of the semifinals will be played on April 24 and 25, with the return games on May 1 and 2.
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