After victories over Sunderland and Tottenham Slaven Bilic’s side came from 2-0 down to win 3-2 against 10 men at Goodison Park thanks to Dimitri Payet’s last-minute goal.
It appeared the Hammers’ Champions League dreams were fading with just 12 minutes remaining but a remarkable late turnaround has put them within three points of third-placed Arsenal.
“We’ve had some amazing results lately - like Spurs on Wednesday, but for team spirit that was fantastic,” said Noble.
“This team spirit, desire and never-give-up attitude we have got is amazing.
“We know we are a good team, we have proved it over the last eight or nine months, but that was a little bit special.
“There are still 27 points to play for. There were a lot of draws but, like we have this week, if you put a few wins together you are back up there.
“To come away with three wins is fantastic and massive credit to the club.”
West Ham’s bubble appeared to have burst after Romelu Lukaku’s 18th league goal of the season was followed by Aaron Lennon’s fifth in seven games.
Even the sending off of Kevin Mirallas for a mindless second bookable offence, having originally been caution for diving, in between appeared to make little difference to the visitors.
Adrian saved a Lukaku penalty which could have made the game safe, allowing Michail Antonio to kick-start the revival in the 78th minute. The momentum it generated got them over the line with substitute Diafra Sakho and the Payet completing Everton’s capitulation.
“Adrian’s save was the turning point in the game and we never looked back,” added Noble.
“I was saying to the lads on the pitch ‘Get a goal’ and it gives you belief and gives them nervousness and we managed to do that.
“We were 2-0 down against 10 men and we could have given up but we never and we deserved our three points for the amount of effort we put in.”
Everton remain as inconsistent as ever. They have won just four of 15 matches at Goodison and it is a problem which shows no signs of easing.
“I am concerned about the amount of defeats we have had at home,” said manager Roberto Martinez.
“At home we should be getting points without playing well.
“The difference in us not pushing for Champions League places this season is the number of defeats we’ve had at home.”
Robles, Stones (Besic 46), Jagielka, Funes Mori, Coleman, McCarthy, Barkley, Oviedo, Lennon (Niasse 76), Lukaku (Barry 89), Mirallas.
Baines, Deulofeu, Osman, Howard
Adrian, Kouyate, Oxford (Carroll 46), Ogbonna, Antonio, Noble, Obiang (Song 61), Cresswell, Lanzini, Payet, Emenike (Sakho 61).
Randolph, Henry, Hendrie, Dobson
Anthony Taylor (Cheshire)