There is an inevitability to Bayer Leverkusen’s late shows. On a night of tension and occasional ill-temper at a bouncing BayArena, where patience was stretched by West Ham’s stifling tactics, the Bundesliga’s champions-elect stayed cool, used their bench and were rewarded for trusting in themselves by scoring twice in the dying stages.

Not for nothing is Xabi Alonso, whose next task is to clinch the first title in his club’s history on Sunday, regarded as management’s rising star. The statistics pointed to Leverkusen dominance, the shot count 33 to West Ham’s one, the possession embarrassing, but it still took persistence for Alonso’s side to take control of this Europa League quarter-final.

West Ham fought hard, the discipline instilled by David Moyes lifting them, and it was still goalless with seven minutes left. But Leverkusen, whose 42-match unbeaten run owes much to their knack of winning late, would not be denied. Jonas Hofmann produced the breakthrough after coming on and Victor Boniface, another of Alonso’s impressive substitutions, gave the scoreline a realistic look by heading home in added time.

It felt like a pivotal goal from Boniface, who scored with West Ham deflated and fatigued, all the chasing sapping their energy levels. Two-nil down to one of the best sides in Europe, the prospect of a turnaround seems remote. West Ham struggled to lay a glove on Leverkusen and, to add to their selection issues, they will have to find a way of attacking without the creativity of Lucas Paquetá, who is banned for the second leg after being booked for a petulant foul on Amine Adli.

“We’re playing a Champions League team tonight – and a good one at that,” Moyes said, although he was less complimentary about the behaviour of Alonso’s coaching team, arguing that their protests convinced the Portuguese referee to caution Paquetá. “I thought it was disgraceful,” Moyes continued. “I’m really disappointed with their bench. They should let the referee make the decision.”

Alonso was unmoved by the criticism. He dealt with a rejig from West Ham, whose lack of depth was highlighted by the absence of Edson Álvarez in midfield and Jarrod Bowen in attack. Moyes used a 4-2-3-1 system and there was early encouragement for the visitors, Michail Antonio surging past Jonathan Tah, only for Mohammed Kudus to shoot tamely at Matej Kovar. It was an isolated foray. Sixteen minutes in, the home fans howled when Lukasz Fabianski delayed a goal-kick. Leverkusen smother opponents and they had already managed five shots by that stage. Fabianski saved well from Alejandro Grimaldo and Adli.

The action flew in one direction, Granit Xhaka controlling midfield, Florian Wirtz and Adli scheming. Starved of the ball, the threat minimal without Bowen, West Ham toiled. Their wing-backs were not in the game. Paquetá’s swipe on Adli – a red card, Leverkusen felt – was a sign of the playmaker’s frustration. He soon risked a second booking.

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Alonso told Leverkusen, who sit 16 points above Bayern Munich, to stay calm. They continued to probe and Patrik Schick’s angled drive tested Fabianski, although there was a different feel as half-time approached. Antonio’s strength unsettled Tah at times. The striker wanted a penalty after tangling with the centre-back.

The crowd began to chunter during the second half, especially as they could see that there was a stodginess to West Ham’s attempts to build. They were uncomfortable when Leverkusen pressed. Tomas Soucek and James Ward-Prowse slogged away in central midfield and Kudus could not showcase his skill.

With 65 minutes gone Paquetá came alive, turning beautifully in midfield, only for his head to drop when Antonio messed up the return pass. An away goal looked unlikely. Moyes said that Konstantinos Mavropanos limping off was a turning point. The centre-back was strong next to Kurt Zouma and Aaron Cresswell.

Challenged to be more direct, Leverkusen went down the flanks, Schick’s header stretching Fabianski. The pressure grew and Boniface caused problems following his introduction. Latching on to a header from a corner, the striker’s shot was blocked by Zouma. The ball dropped to Hofmann, whose hooked shot squirmed through the bodies and past Fabianski.

Leverkusen always find a way. The tension lifted, they pushed for a second. Another cross came in and Boniface extended the lead, giving West Ham a mountain to climb.

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