Filip Kostić's double and Rafael Borré's wonder goal ensured Frankfurt could hold off a late Barcelona comeback to secure a semi-final place.
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Frankfurt are through to the UEFA Europa League semi-finals after surging into a three-goal lead away to Barcelona – and just about staving off a late comeback from the Catalan giants.
4' Kostić thunders a penalty opener
36' Borré hits stunning long-range strike
67' Kostić rifles low effort into far corner
90+1' Sergio Busquets hits thumping drive
90+10' N'Dicka dismissed for second booking
90+11' Depay powers home spot kick
Match in brief: Eagles soar in Camp Nou
The visitors got off to a dream start with Filip Kostić emphatically converting a fourth-minute spot kick, after Eric García had impeded Jesper Lindstrøm.
Barcelona almost levelled shortly after, but Kevin Trapp was equal to Ronald Araújo's snap-shot – and Frankfurt promptly regained control. Indeed, the visitors doubled their lead in emphatic fashion, Rafael Borré sending a thumping right-footed effort into the roof of the net, after their press had disrupted the Barça midfield.
The hosts were the better side after the restart, with Trapp spreading himself well to deny Pierre-Emerick Aubameyang from close range. But Kostić had other ideas and, with just over 20 minutes left, the Serbia winger rifled in a crisp strike for the Bundesliga side's third.
The Blaugrana pressed in their efforts to spark an unlikely comeback, and were almost rewarded in added time via Sergio Busquets' fierce strike and substitute Memphis Depay's penalty, with Evan N'Dicka dismissed for a second bookable offence. It was too little, too late, as Oliver Glasner's men held on to record a famous victory.
Graham Hunter, Barcelona reporter
Not only elimination but a painful way to depart this competition which Barcelona, by their own admission, were intensely keen on winning in Seville next month. Xavi Hernández's squad has performed much better since he took over and played lovely football. However, there still remain specific areas to improve, particularly their ability to compete with direct football and swift counterattacks. The evidence was here – painful, but useful in the medium term.
Semi-finals: 28 April and 5 May
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West Ham vs Frankfurt
Steffen Potter, Frankfurt reporter
With his team having picked up just one of nine possible points from their last three Bundesliga games, Frankfurt coach Glasner has stressed that their goal now should be to qualify for the UEFA Champions League by winning this competition. After tonight's display, you have to say that it's certainly on the cards!
Oliver Glasner, Frankfurt coach: "It was incredible how the lads performed tonight. We made it a bit too exciting in the end, which was unnecessary. Lots of compliments for our boys and our fans. Everyone who could be here tonight will never forget this."
Kevin Trapp, Frankfurt goalkeeper: "Yes, I am [speechless]. Nobody expected this, if you are honest. Everyone expected us to suffer, that they would have lots of possession. We needed to take our chances and today we were very efficient.
Xavi Hernández, Barcelona coach: "We were trying for some heroics at the end, but it wasn't sufficient. We didn't play the best way – in fact, we weren't good tonight. They played well on the counterattack and although their second was a fantastic goal, it stemmed from a very silly mistake of ours."
Ronald Araújo, Barcelona defender: "What a pity to lose this match – notwithstanding the result, we did what we'd been working on in training. It's a pity because they hit us at all the crucial moments. There were errors you can't commit in European football and that's why we're out."
- Kostić's opener was the earliest penalty goal conceded by Barcelona in UEFA competition.
- Aubameyang failed to score in a home appearance against Frankfurt for the first time in his career, at the sixth time of asking.
- Frankfurt are unbeaten in their five UEFA competition away meetings versus Spanish sides, winning four.
- Barcelona suffered their first loss in 16 matches across all competitions.
Barcelona: Ter Stegen; Mingueza (Dest 61), Eric García (L. de Jong 70), Ronald Araújo, Jordi Alba; Gavi, Sergio Busquets, Pedri (F. de Jong 46); Dembélé, Aubameyang (Traoré 61), Ferran Torres (Depay 80)
Frankfurt: Trapp; Touré (Hasebe 90+9), Hinteregger, N'Dicka; Knauff (Chandler 90+9), Jakić, Rode (Hrustic 80), Kostić; Lindstrøm (Hauge 80), Kamada; Borré (Ache 90)
Where is the 2022 Europa League final?
Seville's Ramón Sánchez-Pizjuán Stadium will stage the final on Wednesday 18 May.
The winners gain a place in the 2022/23 UEFA Champions League group stage, if they have not qualified via their domestic competition.