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Bayer Leverkusen set a new European unbeaten record of 49 successive games in securing a late draw with Roma to reach the Europa League final.
Josip Stanisic scored with the last kick of the game in the 97th minute to earn Xabi Alonso's side a 2-2 draw on the night and a 4-2 aggregate victory.
Roma, who had lost the first leg in Italy but were much improved in Germany, drew level in the tie through two Leandro Paredes penalties.
But a disastrous own goal from Gianluca Mancini handed Leverkusen the crucial advantage in the two-legged semi-final - before Croatia defender Stanisic ensured history with the latest in a long line of Leverkusen late goals.
They have now gone 49 successive games without defeat in all competitions, including 40 victories.
It means Leverkusen, who were knocked out by Roma at this stage last season, better the unbeaten run the Eusebio-led Benfica side managed between December 1963 and February 1965.
That feat by the Portuguese giants was the longest unbeaten run since the advent of European competition, according to Uefa - until this remarkable Leverkusen campaign.
Alonso's men, who are seeking a treble this season having won the Bundesliga title and also reached the German Cup final, will face Italian side Atalanta in the Europa League showpiece in Dublin on 22 May.
Stanisic writes Leverkusen into history
The Leverkusen players streamed on to the pitch at full-time, wildly celebrating a remarkable achievement, which they could have secured much earlier in the night had they taken their chances.
They dominated the first half, with Granit Xhaka striking the post from 22 yards before Roma keeper Mile Svilar made a fine double save to deny Adam Hlozek then Amine Adli.
But Roma took the lead against the run of play when Leverkusen captain Jonathan Tah dragged down Sardar Azmoun in the box, with Paredes smashing the resulting penalty down the middle of Matej Kovar's goal.
The same pattern persisted after the break, with Leverkusen having the better chances without scoring. Svilar continued to deny the Bundesliga champions, making a fine one-on-one save from Jonas Hofmann after the break.
And they were punished again when Hlozek handballed from a Roma corner, allowing Paredes to step up and this time score low into the left corner.
Daniele De Rossi's Roma appeared set to force extra time until a nightmare moment with eight minutes remaining. Svilar, who made 13 saves and was otherwise superb, flapped at a corner which flew between his gloves, hit the unsuspecting Mancini in the face at the far post and bounced into the net.
And passage to Dublin - as well as a place in the European football history books - was confirmed when Stanisic cut in from the right and fired low, left footed, past Svilar. It was the 17th goal Leverkusen have scored after the 90th minute in matches across all competitions this season.
Leverkusen become the second German side to reach a European final this week, after Dortmund won their Champions League semi-final to set up a meeting with Real Madrid at Wembley.
