Having won a marathon FA Cup replay after extra-time against Liverpool, the Hammers found themselves 2-0 down with less than half an hour to go at Carrow Road.
Midweek goal hero Michail Antonio’s mistake let in Robbie Brady for the opener and Brady’s international colleague Wes Hoolahan looked to have wrapped up three points for the Canaries.
But Dimitri Payet pulled one back with 16 minutes left before setting up Noble to crash home the equaliser to secure a 2-2 draw.
“The lads put in everything to get the point, which was so important for us, after being 2-0 down,” skipper Noble said.
“Sometimes you’ve got to hold your hands up and we made a mistake, obviously with Michail, but you can’t blame him for that.
“He’s been fantastic for us, and Robbie Brady scored a great goal. But the fight, the character and the spirit we had in coming back was great.
“We scored two really good goals and what a great comeback, especially after winning in the 120th minute against Liverpool. To come back from that just finishes the week off on a good note.”
It was a bitter pill to swallow for Norwich, although Newcastle’s 5-1 defeat at Chelsea later in the day at least allowed them to climb out of the relegation zone.
Manager Alex Neil, whose side had lost their previous five matches, said; “In terms of all-round performance, it was certainly an improvement. We need to go and try and win games and I think you saw that approach.”
Ruddy, Martin, Klose, Bassong, Brady, Redmond, O’Neil, Howson, Naismith (Olsson 76), Hoolahan (Dorrans 85), Jerome (Mbokani 84).
Bamford, Rudd, Jarvis, Ivo Pinto.
Adrian, Byram, Collins, Ogbonna, Cresswell, Noble, Song (Moses 62), Obiang, Antonio (Emenike 70), Valencia (Carroll 62), Payet.
Randolph, Oxford, Parfitt-Williams, Browne.