Marco Silva's side slipped four points adrift of safety in defeat at Leicester City last week, but a third win over the Swans this season has put them back in touch with teams above them, including Saturday's visitors.
Silva's first game in charge was a 2-0 home win over Paul Clement's men in the FA Cup, but this triumph could be all the more significant come the end of the campaign.
Given the high stakes, it was little surprise that the game was a tense affair, but Silva was rewarded for a brave second-half introduction of Niasse, who joined Abel Hernandez up front and scored twice within 15 minutes of coming on.
Hull remain unbeaten at home under the Portuguese, with games at the KCOM Stadium to come against the likes of Middlesbrough and Sunderland suggesting all is not lost for the Tigers.
Wayne Routledge was guilty of wasting the Swans' two best openings, with Alfie Mawson's stoppage-time goal proving too little too late.
The first of those Routledge chances came in just the ninth minute, but Eldin Jakupovic denied Routledge one-on-one after an excellent reverse pass from Gylfi Sigurdsson.
The visitors failed to build on their strong start, however, and Jordi Amat playing in an unfamiliar right-back role after Angel Rangel's injury-enforced withdrawal gave Hull foundations for a revival late in the half.
Left winger Kamil Grosicki gave Amat a stern examination, curling a cross-shot into Lukasz Fabianski's arms before flashing a shot wide and then almost supplying a tap-in for Hernandez, who was bravely denied by a flying Fabianski after being lobbed by his Poland team-mate.
The in-form Fernando Llorente was also forced off before the break with a dead leg, and Clement was visibly angered when Routledge again wasted a good chance to score, blazing high and wide after Jakupovic palmed Tom Carroll's cross back into danger.
Jakupovic was called into action at full stretch from a Sigurdsson free-kick, prompting Silva to bolster his attacking options by replacing Alfred N'Diaye with Niasse and the Tigers immediately had more bite, but Grosicki could not take advantage after rounding Fabianski inside the box.
However, the move paid dividends soon after as Niasse burst clear on the end of a return ball from Hernandez and finished calmly past the onrushing Fabianski.
And the Senegal striker sealed the win nine minutes later, latching onto Ahmed Elmohamady's cross to blast past Fabianski from close-range.
Mawson continued his fine run in front of goal with a 91st-minute header from Sigurdsson's free-kick, but the earlier missed chances may come back to haunt a Swans' side that have lost every away game in which they have conceded first this term.
KEY OPTA STATS
- All three of Oumar Niasse’s Premier League goals for Hull City have been as a substitute.
- The Swans have lost their last three visits to the KCOM Stadium, each in a different competition.
- Swansea have now shipped 61 goals this season. No side to have conceded 60+ goals after 28 games of a Premier League season has stayed up.
- Swansea have now conceded more goals in the final 30 minutes of games than any other Premier League side this season (29).
- Niasse is the fourth substitute to score twice in a Premier League game this season, and first since Fernando Llorente against Crystal Palace in November.
- The Tigers have won three of their four Premier League home games under Marco Silva (D1), the same number they’d won in their previous 16 at home in the competition.