Frankfurt go through to the last four and the German club will now be eyeing a first European triumph since they won the UEFA Cup in 1980.
Barcelona has been dumped out of the Europa League as Eintracht Frankfurt pulled off a shock 3-2 victory at Camp Nou to progress to the semi-finals.
After the first leg finished 1-1 in Germany last week, Barca were strong favourites to win at home against a side sitting ninth in the Bundesliga.
But Frankfurt, inspired by an incredible travelling support of around 20,000 fans, outplayed the Catalans on Thursday, Filip Kostic scoring twice, the first an early penalty, either side of a stunning long-range strike by Rafael Santos Borre.
Sergio Busquets pulled one back for Barcelona in the 91st minute and then Memphis Depay scored a penalty in the 11th minute of injury time as the hosts attempted a late comeback.
But it was too little, too late as Frankfurt sealed a momentous 4-3 aggregate win.
They will face West Ham in the last four after the Premier League side cruised past Lyon.
"It's a hammer blow for us. They deserved to go through," said Barcelona coach Xavi Hernandez, who was also unhappy at the number of away fans inside the stadium.
"Obviously it didn't help us," Xavi added.
"It was like a final, the fans evenly divided. The club is checking what happened but it was an error on our part."
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Possibility of first European triumph in 40 years
Instead, Frankfurt go through to the last four and the German club will now be eyeing a first European triumph since they won the UEFA Cup in 1980.
"What we have experienced today no money can buy," Frankfurt coach Oliver Glasner said.
"These emotions will last forever."
Barcelona were undefeated since December in all competitions and have surged up to second in La Liga after thrashing Real Madrid 4-0 at the Santiago Bernabeu less than a month ago.
While that run means Barca should no longer need the Europa League to qualify for the Champions League next season, this was a great chance for Xavi to add a trophy to what has been an impressive first few months as coach.