After suffering a 2-0 defeat in the first leg, West Ham are 10/1 to overcome Bayer Leverkusen and reach the Europa League semi-finals.
The Hammers were successfully stifling their unbeaten German opponents until their resolve was finally broken by a Jonas Hofmann strike after 83 minutes.
Their woes were compounded in stoppage time as Victor Boniface doubled Leverkusen's advantage, leaving David Moyes' side with a mountain to climb if they're to progress to the final four of the competition.
West Ham are now 20/1 to reach the final of the competition in Dublin and 33/1 to lift the Europa League trophy.
Overcoming a Leverkusen side who are yet to taste defeat this season was always going to be a daunting challenge and yet West Ham were able to frustrate Xabi Alonso's charges, who dominated possession but struggled to carve many gilt-edged opportunities.
Disciplined and resilient, the Hammers required a series of smart saves from Lukasz Fabianski to keep the scores level, with his stop to deny a Patrick Schick header in the second half arguably the pick of the bunch.
But one of the reasons why Leverkusen are on the verge of their first Bundesliga title is their persistence and the pressure eventually told, with Hofmann's volley splitting a sea of bodies in the penalty area and nestling into the bottom corner.
Leverkusen turned the heat up on their opponents in the closing stages and they were rewarded with a second in stoppage time. A short corner routine gave Hofmann time to whip in a cross and he found Boniface, who directed his header beyond Fabianski.
West Ham did lose the first leg against SC Freiburg before romping to a 5-0 in the second leg, but it's going to take something special from Moyes' outfit to prevail in this tie, with Leverkusen as short as 1/20 to progress to the semi-finals.