The away side peppered the woodwork with attempts but eventually came undone thanks to the midfielder's accuracy from the spot with just 11 minutes remaining
Despite losing their last six away games in the Premier League, drawing a blank in the previous four, Mike Phelan's men produced an excellent display at London Stadium and were repeatedly denied a goal by the narrowest of margins.
But the decisive moment arrived 14 minutes from time, when referee Lee Mason saw fit to award the hosts a questionable penalty and Noble converted.
A deflated Hull could muster no response as they slumped to the foot of the table for the first time this season.
Tigers goalkeeper David Marshall went down injured inside the opening 10 minutes, but remained on the pitch despite reporting a groin injury.
Dimitri Payet carried the Hammers' greatest threat in the opening exchanges and the Frenchman's jinking run ended in a shot that was blocked by Curtis Davies.
But it was the visitors who went closest to a first-half goal, with Mbokani collecting Aaron Cresswell's poor 21st-minute backpass and beating Darren Randolph, only to see his effort hit the inside of the post and stay out

