Having won a marathon FA Cup replay after extra time against Liverpool on Tuesday, 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 Wes Hoolahan looked to have wrapped up a precious three points for the struggling Canaries.
But West Ham refused to throw in the towel and Dimitri Payet pulled one back with 16 minutes remaining before setting up Noble to crash home the equaliser to secure a 2-2 draw
"Especially after the midweek game, the lads put in everything to get the point, which was so important for us after being 2-0 down," skipper Noble told West Ham TV.
"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 scored a great goal. But the fight, the character and the spirit we had in coming back was great. We probably should have won it in the end. We were gutted in there that we hadn't won.
"We scored two really good goals and what a great comeback for the club, especially after the winning in the 120th minute against Liverpool. To come back from that just finishes the week off on a good note."
Source: PA