Despite dominating the game in a possessional sense, it was the away side who posed the greater threat going forward in the opening exchanges.
They could have found themselves ahead inside just nine minutes through Wayne Routledge after Gylfi Sigurdsson slotted the ball between Hull duo Andrew Robertson and Harry Maguire to release the winger.
However, Routledge's side-footed shot was well dealt with by Eldin Jakupović, who deflected the ball out for a corner.
Following an early scare, Marco Silva's side began to turn the screw and were the better side for the majority of the match. Tom Huddlestone was the first to call Lukasz Fabianski into action just shy of the quarter hour mark with an effort from 20-yards out.
Sam Clucas then wasted a free-kick in a promising area for the hosts before Lazar Marković's delightful cross-field ball to Robertson was squared to Kamil Grosicki who's shot was well dealt with by Fabianski. For all their dominance, the score-line remained level.
The game continued in a similar pattern for the second-half, where Markovic'c cross needed a strong header from Federico Fernández to clear the danger under his own crossbar. Fabianski was on hand to deal with Huddlestone's follow up and keep the scores level.
However, bringing on Oumar Niasse proved to be the difference between the two sides, with the substitute netting just six minutes after entering the fray when he latched on to Abel Hernandez's pass before slotting cooly past Fabianski.
The forward soon doubled his tally nine minutes later with a close range finish from Ahmed Elmohamady's cross.
A late-injury time goal by Alfie Mawson made it a slightly more nerve racking finish at the KCOM Stadium, but the hosts' dominance was duly rewarded with a very important three points.
Despite remaining at the bottom-of-the-table, Hull are now just one point from safety and have moved within three points of Swansea, who are in 16th.
Everton reject, Hull hero
Oumar Niasse was cast away on the sidelines for Everton eight months ago. Reduced to training with the Under-23s by Ronald Koeman last summer, Niasse made the move to Humberside, where he has enjoyed much better fortunes.
The 26-year-old gave Hull the quality they were lacking in the final third here, delivering two absolutely massive goals for his team. Silva's decision to replace Alfred N'Diaye with Niasse proved to be a tactical masterstroke, with the forward showing exactly what he is capable of when it matters most.
Doubling his Premier League goal tally for the season, Niasse displayed what a crucial part he could play for Hull in the remaining fixtures if they want to avoid the drop.
Different result on a different day?
For all their dominance and possessional superiority on Saturday afternoon, Hull could easily have come off second best against Swansea.
Routledge wasted a golden opportunity for his side after Jakupović parried Tom Carroll's cross when the scores were level.
However, the main bit of controversy arose when N'Diaye rather abruptly halted Sigurdsson's charge by pushing him from behind.
Having already recieved a yellow card for a needless challenge earlier on in the game, the midfielder was lucky not to see red and on another day, it could have made all the difference for Swansea.
Silva the right man for the job
Hull were bottom-of-the-table and three points adrift when Marco Silva took charge in January.
Fast forward nine weeks from his first game in charge, the Tigers find themselves just one point from safety with 10 games still to play.
Silva has been pivotal to Hull's upturn in form and fortunes since taking the reigns, with the Portuguese boss recording three Premier League wins at the KCOM - the same amount they had won in their previous 16.
With huge games against Middlesbrough and Sunderland still to be played at the KC, their home form could be crucial to their Premier League survival. A task that looked so impossible when he took charge is becoming an increasing possibility for Hull fans.