Noble and Manuel Lanzini were on target for the Hammers in the first half at Vicarage Road, but Gerard Deulofeu hit back almost immediately after the restart.
Jose Holebas was then shown a straight red for bringing down Michail Antonio, ruling him out of next weekend's FA Cup final against Manchester City, and Marko Arnautovic's effort and Noble's penalty completed a scoreline that was somewhat harsh on Watford.
Defeat means Watford miss out on finishing in the top 10 in the top flight since 1986-1987, with the Hammers leapfrogging its opponent at the last.
West Ham withstood an early Watford onslaught, which included Deulofeu seeing a goal rightly ruled out for offside after 17 seconds, to take the lead.
Noble played a give-and-go with Antonio, jinked past Christian Kabasele and coolly slotted past Ben Foster.
West Ham doubled the lead after 39 minutes. Antonio showed great tenacity before hitting a stinging 20-yard effort that was tipped onto the bar by Foster, only for Lanzini to nod home the rebound.
Lukasz Fabianski stopped Watford from pulling a goal back before the break with a point-blank save from Troy Deeney, but the lead was halved just 11 seconds into the second half.
Pablo Zabaleta's poor pass was pounced on by Deulofeu, who cleverly nicked the ball past Fabianski to finish into an open goal.
But the Hornets were stung by Holebas' red card, the full-back tripping Antonio and deemed to have denied a clear goalscoring opportunity.
There was no way back for Watford when Arnautovic had a simple tap in after Felipe Anderson's low strike rebounded off the post, with Noble emphatically rounding out the scoring from the spot after Kiko Femenia clumsily tripped Antonio.