Having held on for a 1-1 first-leg draw in London after playing the entire second half with 10 men, David Moyes' players withstood periods of intense early pressure before sweeping their Ligue 1 opposition aside.
The visitors struck twice in seven minutes at the end of the first half, as Craig Dawson met Pablo Fornals' corner with a superb near-post header before a deflected Declan Rice strike put the Premier League club in total charge.
Jarrod Bowen extended the advantage within three minutes of the restart, slotting in at the end of a sweeping counter-attack, and a deflated Lyon could offer no response as West Ham comfortably saw out a memorable win.
Rice later said: "It's special. Very, very special. We knew it was a tough place to come, but we knew with what we had on the pitch, our attacking players and what we had seen in the first game with them defensively, we could score goals tonight.
"To get a 2-0 lead and then come out early in the second half and Jarrod to put that one in the net is a special feeling. For all the fans, it is such a great night.
"When it is half-time and it is 2-0 your heart is racing. You're thinking about it still being 0-0 as you need to go out and give another string performance.
"If you can't get up for these games you shouldn't be playing. The roar from the warm-up, it was spine-tingling and it gives you that fire in your stomach.
"Their Twitter admins were saying they don't know how they are not going to beat us, but those things come back to bite you. We put in a performance and now West Ham are in the semis.
"For Frankfurt to beat Barca, they are a good side. We will be ready for whatever. We want to reach the final."
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