For the second time in three days Noble stepped up to the spot to secure an unconvincing, but very welcome, victory for the Hammers.
But Hull will wonder how they left the London Stadium empty-handed
They have now not scored away from home for eight-and-a-half hours but will not come much closer after being denied by the woodwork three times and seeing an effort cleared off the line
West Ham, in contrast, were abject but nevertheless picked up a fifth win of the season, all of which have been by the same scoreline
In the early stages Hull keeper David Marshall had looked as though he might have to be substituted after pulling up with a groin problem
But he opted to stay on and West Ham sportingly ensured he did not have to exert himself, with a tame 30-yard Dimitri Payet free-kick their only effort on goal in the first half.
However Hull created a host of presentable chances, the first of which was all West Ham's doing.
Aaron Cresswell's woefully under-hit backpass played Dieumerci Mbokani in one-on-one with Hammers keeper Darren Randolph but his effort clipped the inside of the post and rolled across goal to safety
Moments later Randolph did well to palm Harry Maguire's powerful header wide, before Sam Clucas fired too high and Mbokani volleyed over.
Randolph then kept out Maguire's shot before the same player threatened again, this time denied by Pedro Obiang's interception which almost rolled into his own net.
The hosts trooped off at half-time to boos from some home fans and no doubt met with an angry boss in Slaven Bilic, who hauled off the ineffective Manuel Lanzini and Obiang at the break.
Andre Ayew and Edimilson Fernandes were the ones sent on to sort out the mess, but somehow things threatened to get even worse with Noble heading Andrew Robertson's cross against his own post.
Robertson then took aim from just inside the area only to see his angled drive crash back off the opposite post.
West Ham threatened when Ayew's header was cleared off the line by Robertson, before a carbon-copy effort at the other end from Maguire was hacked away from under the crossbar by Fernandes.
But in the 76th minute Hull were left crestfallen after Michail Antonio went down in the area under close attention from Tom Huddlestone, and referee Lee Mason pointed to the spot.
Noble had missed his spot-kick against Burnley on Wednesday, only to tuck in the rebound, but he made no mistake this time and West Ham emerged with another three points
Source : PA