The Hammers clinched their spots in the Europa League quarter-finals with the extra-time win after Tomas Soucek had put them ahead in the 39th minute from Michail Antonio’s cross.
Soucek hit the side netting with a close-range header in extra time before Yarmolenko fired home a 112th-minute rebound after Pablo Fornals’ shot had been saved.
Yarmolenko had been on compassionate leave given the Ukrainian-Russian conflict but was used as a 87th-minute substitute before netting the dramatic winner.
“It must be incredibly difficult for him, and once again hopefully the world will see a Ukrainian footballer doing well in Europe it will be all around Europe and from that point of view hopefully the message is getting to everybody that we don’t want this war and we want Russia to stop,” Moyes told reporters.
On the magnitude of the win and achievement, Moyes added: “Atletico Madrid beat Manchester United, Villarreal beat Juventus, so don’t underestimate the quality of the Spanish sides, especially Sevilla who continually win this competition and are really difficult to play against.
“If you want to be a big club, you have to get used to being in all the time. We are climbing a mountain but we are base camp at the moment.”
Elsewhere in the Europa League Round of 16, Pedri and Pierre-Emerick Aubameyang netted as Barcelona progressed via a 2-1 win at Galatasaray after a 0-0 draw in the first leg.
Rangers lost 2-1 at Red Star Belgrade but progressed 4-2 on aggregate, while Atalanta’s 1-0 road win at Bayer Leverkusen sealed a 4-2 aggregate triumph.
Sporting Braga got past Monaco, Olympique Lyon edged FC Porto, Eintracht Frankfort narrowly defeated Real Betis and RB Leipzig had won on walkover against Spartak Moscow due to their suspension from the Russian invasion of Ukraine.