Eintracht Frankfurt reached their first European final for 42 years after a 1-0 home win on Thursday over 10-man West Ham sealed a 3-1 aggregate victory in their Europa League semi-final.
West Ham had left-back Aaron Cresswell sent off early on and Hammers manager David Moyes was also dismissed from the sidelines with 12 minutes left for arguing with the referee.
"A sending off is always going to make it a mountain to climb, we had genuine belief that over two legs they weren't going to beat us," said West Ham captain Declan Rice.
"We just played a team that played a similar way to us and it caught us out. We're gutted."
Colombia striker Rafael Borre netted the first-half winner on the night to book Frankfurt a place in the Europa League final on May 18 in Seville against Scottish giants Rangers.
"A dream has finally comes true," said Eintracht club president Peter Fischer.
"This city deserves it. And now we're going to win this thing."
Borre scored just after Cresswell was sent off, leaving the visitors a man down for more than an hour and needing to score twice just to force extra time.
Frankfurt had been dealt an early blow when key defender Martin Hinteregger limped off with a leg injury.
When a long ball put Frankfurt's Jens Hauge into space, Cresswell pulled back the Norwegian, who went down just outside the area.
Cresswell, who was also sent off in the quarter-final first leg against Lyon, was initially only booked, but referee Jesus Gil Manzano brandished the red card after a VAR review.
Moyes responded by swapping Ben Johnson for forward Manuel Lanzini.
Yet Frankfurt went ahead in the 26th minute.
When the hosts attacked down the right flank, Ansgar Knauff's cross found Borre, who fired home unmarked in the area.
Dogged defending in the second half restricted Frankfurt to just a handful of chances for Knauff and Filip Kostic, who caused havoc on the left.
West Ham had chances of their own and as the visitors pushed for an equaliser, Manzano banished Moyes to the stands after the Scot lost his temper.
Frankfurt, who lost to Chelsea on penalties in the 2019 Europa League semi-finals, are into their first European final since winning the UEFA Cup in 1979/80.
"That was an evening you never forget," beamed Frankfurt coach Oliver Glasner. "The squad was exceptional."