The 26-year-old, on loan from Everton, was brought on for Alfred N'Diaye in the second-half and within six minutes got the opening goal of the match, latching on to Abel Hernandez's pass before slotting cooly past Lukasz Fabianski.
Nine minutes later, the striker doubled his tally, finishing well from Ahmed Elmohamady's cross to put Hull in command.
An injury-time goal from Alfie Mawson proved to be nothing more than a consolation goal for the away side, who are now just three points ahead of Marco Silva's men.
While Hull remain in the bottom three, they are just one point from safety and the once impossible job to try and avoid relegation, is looking increasingly possible for the Tigers.
Eldin Jakupović - 6 - Almost had a nightmare moment in the first-half when he flapped at Tom Carroll's corner, only for Wayne Routledge to waste the golden opportunity. The goalkeeper struggled to deal with high balls into the box, but did produce some tidy saves, especially in a one-on-one situation with Routledge.
Omar Elabdellaoui - 7 - Brought some assurance to the right back role, while providing a threat going forward. Credit has to go for him for the attack that brought about Niasse's opener.
Andrea Ranocchia - 7 - Used his experience well in the heart of defence to provide a calming and composed figure at the back for Hull. Dealt well with Swansea's balls into the box.
Harry Maguire - 6 - Was outshone by his defensive partner. A cross field ball that was poorly executed almost left his side in real trouble, but he reacted well to recover. The injury to Llorente made his second-half a lot easier than it could have been.
Andrew Robertson - 7 - Provided an attacking threat down the flank for Hull, but was almost caught in the first-half following Sigurdsson's through ball that found Routledge in behind.
Lazar Marković - 7 - Flashes of brilliance from the Liverpool loanee, whose cross-field ball led to a great chance for Grosicki. However, he failed to provide a continued threat and there is still a feeling that his best is yet to come.
Alfred N'Diaye - 5 - Lack of discipline could have cost Hull dear on another day, with a blatant push on Sigurdsson going unpunished. Withdrawn just after the hour mark and produced a rather sloppy performance.
Tom Huddlestone - 8 - At the heart of everything good within Hull's midfield and set the pace for the game with an early effort on goal, although it was relatively straight forward for Fabianski. Improved as the game wore on and helped keep up the pressure on the away side.
Sam Clucas - 6 - Had a relatively quiet game in midfield and didn't seem entirely comfortable during the game. Improved after N'Diaye was replaced which saw Clucas take up a deeper role.
Kamil Grosicki - 6 - Missed a golden opportunity in the first-half and was wasteful throughout in front of goal. In terms of crossing, there was also much to be desired. However, in the first hour, he was the one that stretched Paul Clement's side the most.
Abel Hernandez - 7 - Produced a delightful assist for Niasse's opening goal while contributing to the second. Much improved when Niasse entered the fray.
Oumar Niasse - 8 - Produced two huge goals that could be the difference between Premier League survival and relegation for Hull come the end of the season. Unlike his teammates, he showed quality in front of goal to tuck away his chances well. Turned the game on its head when it mattered most.
Ahmed Elmohamady - 6 - Produced an assist for Hull's second goal after replacing Marković in the second half.
David Meyler - 6 - Helped to keep the midfield tight and ensure Swansea weren't allowed a way back into the match.