Late strikes by Bayer Leverkusen substitutes Jonas Hofmann and Victor Boniface earned the Bundesliga leaders a two-goal advantage over West Ham and they remained undefeated this season with 37 wins and five draws across all competitions.
Leverkusen dominated the game but the visitors' keeper Lukasz Fabianski pulled off a string of saves and kept out dangerous efforts by Alejandro Grimaldo and Patrik Schick to keep the scores level at the break.
Hofmann gave Leverkusen the lead in the 83rd minute, scoring with a first-time effort and striker Boniface doubled the advantage in stoppage time with a header into the bottom corner.
The hosts, who can clinch the Bundesliga title on Sunday, had 33 attempts on goal -- 13 on target -- compared to one sole effort by midfielder Mohammed Kudus for Europa Conference League holders West Ham.
Roma upset hosts Milan as Gianluca Mancini scored to end the capital club's nine-match winless run against Stefano Pioli's side.
Roma, who had last beaten Milan in 2019, took the lead thanks to Mancini's pinpoint header from Paulo Dybala's corner in the 17th minute.
"We should have been more courageous," Milan coach Stefano Pioli said. "We created some chances, but I didn't see the same quality as in the last matches.
"This team can do more, I know that. I didn't expect the defeat, we weren't precise, we lacked the flair."
Portuguese champions Benfica claimed a 2-1 home win over Olympique de Marseille through goals by Rafa Silva and Argentine forward Angel Di Maria.
The second legs will be played next Thursday.