Bayer Leverkusen will be waking up with sore heads again. Their treble hopes remains alive, as does their sheen of invincibility, but only just. After the beer-stained celebrations that followed their regal charge to the Bundesliga title, Xabi Alonso’s side looked groggy on a pulsating night at the London Stadium and can count themselves lucky to be in a Europa League semi-final against Roma after beating West Ham 3-1 on aggregate. The home fans responding to Jeremie Frimpong’s late equaliser extending Leverkusen’s unbeaten run to 44 matches with rueful applause spoke volumes. West Ham gave everything in their pursuit of a comeback and had the chances to turn the tie around after taking an early lead through Michail Antonio. It was not enough to prolong West Ham’s third consecutive European campaign. David Moyes, whose contract expires at the end of the season, could only look back with pride. His future is up in the air, last year’s triumph in the Europa Conference League fading from view, and although a change of direction is on the cards this performance was a reminder of how brilliant Moyes has been for West Ham. They were powerful and intense from the start, which kept a boisterous home crowd noisy and engaged, and stopped Leverkusen from building any momentum. Alonso, whose side have made a habit of hoarding possession, had to be worried when the woeful Odilon Kossounou lost possession and picked up an early booking for wiping out James Ward-Prowse. It was impossible to tell that Leverkusen were Europe’s most in-form side. Then again, perhaps Moyes was on to something with his pre-match comments about the visitors having a few too many drinks after their historic title win last weekend. West Ham, refusing to be weighed down by the absence of the suspended Lucas Paquetá in attacking midfield, hunted down every sign of lethargy. Their reward arrived after 13 minutes. Leverkusen were pinned back and Tomas Soucek headed Josip Stanisic’s weak clearance to Jarrod Bowen. The winger, who passed a late fitness test on the spine injury that kept him out of the first leg, exchanged passes with Vladimir Coufal before crossing to the far post, where Antonio lost Kossounou and headed past a flapping Matej Kovar. Their aggregate lead halved, Leverkusen looked stunned. West Ham ripped into them, Ward-Prowse pressing hard, the German side increasingly skittish. Mohammed Kudus, dribbling in from the left, shot at Kovar. Antonio spurned a header and almost reached a fizzing cross. Moyes collapsed in disbelief when Kovar made an astonishing save from Bowen, then when Edson Álvarez’s shot hit Antonio. The tension floated to the touchline. A row midway through the half ended with red cards for Billy McKinlay, West Ham’s assistant coach, and Sebastián Parrilla, a member of Leverkusen’s backroom staff. Alonso, observing it all, had already put Kossounou out of his misery. The centre-back was either going to get a second yellow or give away another goal before being replaced by Edmond Tapsoba. Leverkusen needed half-time. Alonso made his next move, swapping out Patrik Schick and Nathan Tella for Victor Boniface and Frimpong. West Ham, who had rejigged their defence when Angelo Ogbonna came on for Nayef Aguerd, had an escape when Florian Wirtz miscued Frimpong’s cross. There was a different feel, Leverkusen showing more poise, albeit without convincing. They remained edgy and could have conceded when Piero Hincapié made a mess of dealing with a long ball down the right. Bowen stole possession but dragged his shot wide. Too many chances went begging and the problem for West Ham was that they lacked options on a bench that contained six academy players. They grew leggy, their inactivity during the January transfer window coming back to bite them. The threat had disappeared by the end. Leverkusen poured through on the break and Frimpong blazed over. Alonso could not relax. The relief was huge when Frimpong’s deflected shot spun off Aaron Cresswell and beat Lukasz Fabianski with two ­minutes left.