Noble put the Hammers in front against Villa with a 45th-minute penalty but Ashley Young levelled six minutes after half-time.
Substitute Zavon Hines fired the winner in injury time to lift the struggling side out of the bottom three.
Noble, still only 23, is in line to make his 100th league outing against Everton on Sunday.
"Wednesday was important," said Noble. "I can say the moments I have been through with this club that was emotionally one of the best moments I have had.
"It was so good to be involved with that. It was a really tough game, really tough, but in the end I thought we deserved it. The confidence is up for Everton. We will rest well, train well and hopefully the fans will turn up like they did against Villa. It will be fantastic if they get behind us and drive us on to another win."