Xabi Alonso’s side was backed by a vocal home crowd at the BayArena and quickly took control of possession.
The Hammers defended resolutely, though, and they also showed an early threat of their own on the break through a blistering Michail Antonio run before Mohammed Kudus hit a tame effort.
Leverkusen continued to pass patiently and incisively, but Lukasz Fabianski denied Amine Adli’s curling effort and James Ward-Prowse blocked strikes from Exequiel Palacios and Edmond Tapsoba.
Fabiański then made an impressive stop to deny Álex Grimaldo’s dipping shot from range in the 20th minute.
There was still a blow for the Hammers as Lucas Paquetá fouled Adli and was shown the yellow card that keeps him out of the second leg, which also resulted in a coming together between the two sets of players.
The hosts kept probing but their frustrations in front of goal continued as Fabiański got down well to deny strikes from Patrick Schick and Tapsoba, before Antonio battled to get into another promising position and saw his cross cleared by Josip Stanišić.
The second half continued in a similar pattern to the first with David Moyes’ side refusing to be broken down while Antonio battled for every ball that came close to him.
They suffered another blow as Emerson Palmieri joined Paquetá in Artur Soares Dias’ book for a foul on Adli, so is also suspended for the second leg.
Jeremie Frimpong fizzed an effort into Fabiański’s gloves from a tight angle, before the goalkeeper pulled off another eye-catching stop to tip Shick’s header over the crossbar as the pressure continued to mount.
Die Werkself eventually made their breakthrough in the 83rd minute, when Jonas Hofmann finished after Kurt Zouma had blocked an effort from his fellow substitute Victor Boniface.
The striker then scored a header of his own from Hofmann's pinpoint cross to double their lead as Leverkusen continued the record of winning each of their home UEL matches this term. They also inflicted the second defeat in West Ham’s last four, giving the Hammers an uphill task at London Stadium.
Flashscore Man of the Match: Jonas Hofmann (Bayer Leverkusen)
