Marco Silva's Tigers had looked fairly toothless until Senegal international Niasse was introduced in the 63rd minute and it proved an inspired substitution from the Portuguese manager.
Within six minutes, Niasse had been played in by Abel Hernandez before slotting the ball beneath Lucasz Fabianski and he then sent the KCOM Stadium into further raptures with another clinical finish 12 minutes from time.
Manager Paul Clement, who has overseen Swansea's remarkable recent resurgence, suffered a miserable afternoon as he lost his top scorer, Spanish international Fernando Llorente, to injury and then had to watch Alfie Mawson's injury-time goal count as a mere consolation.
Hull were still left in the bottom three but their victory saw them leapfrog Middlesbrough into 18th place and move to within three points of Swansea.
(Reporting by Ian Chadband; Editing by Rex Gowar)
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