Said Benrahma swerved a shot past David De Gea to give the Hammers a second-half lead but our keeper made some important saves as we managed to keep on track for another Wembley appearance.
The Reds will meet Fulham at Old Trafford in the last eight of the competition, as we bid to repeat our success in the other domestic cup at the weekend.
Garnacho came out on top in the poll on our official App after also collecting the Emirates award handed out on ITV for the star man.
The Argentina Under-20 international not only bent a superb strike past Alphonse Areola to edge the Reds in front in the 90th minute but his wing wizardry was a constant source of menace to the visiting defence.