The Hammers scored first through Diafra Sakho in the 10th minute but were pegged back when Anthony Martial levelled early in the second half before the French striker had United ahead with a fine finish in the 72nd minute.
Noble said after the match: "It was written in the stars three fantastic goal and sheer determination and will not to lose.
"I am so proud of the players. It was phenomenal. With this team I never feel like we will lose, apart from last Saturday (against Swansea City). We just have that spirit.
"In years gone by we would have lost that game but it written into the stars for this fantastic place."
The victory has West Ham sitting sixth on the Premier League table on 62 points, one point behind fifth-placed United, with one fixture remaining.