Victor Boniface then doubled the lead in the first minute of injury time with a well-directed header from Hofmann's cross.

Alonso's hosts dominated possession but were largely frustrated by a superbly organised Hammers defence until Hofmann's late intervention.

"We have half a chance in the second leg," Moyes told TNT Sports.

"It's going to take some performance because they're a really good team. You never know what's going to happen.

"Let's try to get one and then see if we can get two. We'll pick ourselves up for next week and hopefully get the crowd behind us."

The visitors showed great discipline to limit Leverkusen's chances for much of the game while also offering a threat on the counter through the pace and power of Michail Antonio.

Antonio created arguably the best opportunity of the first half as he broke down the left and squared for Mohammed Kudus, but the Ghana winger's shot was straight at Leverkusen goalkeeper Matej Kovar.

West Ham did need a couple of very smart saves from Lukasz Fabianski to keep Leverkusen at bay for as long as they did.

The 38-year-old keeper got down well to deny Patrick Schick in the first half before leaping to tip the striker's header over the bar in the second when he looked to have been wrong-footed.

Hofmann finally found a way past Fabianski and when Boniface nodded in the second, Leverkusen were assured of victory to stretch their unbeaten run to 42 matches.

Big ask for Hammers after plan comes unstuck late on

David Moyes' strategy was evident from the off. West Ham were content to sit deep, frustrate their hosts and look to break when the opportunity arose.

They so nearly executed it to perfection, with Leverkusen failing to create any clear chances in the first hour or more.

"We'd like to have played more attacking. The players did a brilliant job with the structure," Moyes added.

"But we played against a Champions League side and we're not quite at that level."

Ultimately, though, the pressure told and the Hammers must now end the German side's unbeaten run - and do it in some style - to progress.

That Antonio was a nuisance throughout and caused defender Jonathan Tah plenty of problems will give them encouragement, while getting Jarrod Bowen back fit for the second leg would also be a huge boon.

Even more so given they will be without Emerson Palmieri and, crucially, Lucas Paqueta through suspension after they were yellow carded.

"We have to recognise what we're playing against," Moyes said. "We'll have to do exceptionally well to get that result."

West Ham overturned a first-leg deficit to beat German opposition handsomely in the last round.

A repeat will take some doing but all is not lost - and if they can score the first goal at London Stadium next week, belief will soon return to a Hammers side that is increasingly savvy in European competition.

Leverkusen leave it late again

The German top-flight leaders have made late goals a habit this season and scored twice deep into stoppage time to beat Qarabag in the last 16.

This wasn't quite as dramatic but they were still made to wait by a stubborn West Ham side.

Despite that, though, Leverkusen never showed any sort of panic as they attacked the Hammers relentlessly, looking for any space to exploit around the penalty area.

"We believe in ourselves that we have the quality to score in every minute we can," Leverkusen midfielder Granit Xhaka told TNT Sports.

"Against teams like this and the others who come to the BayArena, it is always difficult to find space because they sit so deep."

As it was, it took two set-pieces break down the visitors, with Hofmann shinning a volley through a crowded penalty area after the initial ball in was not cleared.

He then provided the cross following a short corner with Boniface rising highest at the back post to head home his 17th goal of the season.

"It wasn't easy. They were very deep and always had a lot of players in the penalty area," Alonso added.

"We waited for our moment - and it came, albeit late."

The job is not done for Alonso's team but they know how to win - and with a healthy advantage going into the second leg, they will be confident of advancing to the semi-finals.