West Ham will have to come from behind in Germany next week if they are to reach their first European final in 46 years after Eintracht Frankfurt secured a deserved first-leg advantage at London Stadium.
Jarrod Bowen came agonisingly close to snatching a draw for the hosts in stoppage time when his overhead kick from a Declan Rice cross bounced down off the crossbar.
But that would have been harsh on Frankfurt, who were a constant threat on the counter-attack and showed why they had won away at Real Betis and Barcelona already in the knockout stages.