Hull, who made seven changes to their starting line-up and handed starts to academy players Jarrod Bowen and Josh Tymon, produced a performance full of heart, desire and character as they started off life without Robert Snodgrass in determined fashion.
A contentious 36th-minute penalty from Tom Huddlestone, after Marcos Rojo was deemed to have pushed Harry Maguire, provided Hull with a deserved first-half lead as the midfielder became the first player to score against United in five matches since May 2014.
It was just reward for Hull, with Niasse in particular posing problems and going close earlier after seeing a fierce drive tipped over by David De Gea, who started alongside Zlatan Ibrahimovic, Chris Smalling, Paul Pogba and Marcus Rashford.
United improved after an inhibited first half and after appeals for a penalty were turned down after Smalling went down under pressure from Huddlestone, the Hull midfielder played an inadvertent hand in the visitors' relieving 66th-minute leveller.
His clearance was diverted into the direction of Pogba, who slid the ball home from close range.
Hull refused to be daunted and pushed United in the final 15 minutes and after heading against the bar, Niasse got his reward when he turned in David Meyler's low cross with five minutes to go.
Despite the cajolement of home supporters in the 16,831 crowd, Hull could not take the game into extra-time but could be mighty proud of their valiant efforts as they bowed out with honour and provided encouragement for the key battles ahead..