The home side were second best for large parts of this game until the Everton loanee turned the game on its head with two goals in the space of nine minutes.
With the game locked at 0-0 and Swansea looking the most likely to nick it, Hull boss Marco Silva threw on Niasse on 63 minutes and he made an immediate impact when he exchanged passes with Abel Hernandez before racing clear and slotting home the opener six minutes later.
Niasse then pounced again on 78 minutes when Ahmed Elmohamady’s cross found its way through to the Senegalese forward who made no mistake from close range.
Up until that point Swansea had been the better team and looked the most dangerous. They should have been ahead as early as the ninth minute when Leroy Fer played a lovely ball inside full-back Andy Robertson for Wayne Routledge to cut in on goal but Hull keeper Eldin Jakupovic saved well with his right leg.
The winger then had another golden opportunity in the 54th minute as Swansea, similar to the first half, started the second period much the better side.
Tom Carroll’s pull-back across the six-yard box was pushed into his path by the diving Jakupovic but with the goal gaping and under pressure from Harry Maguire he blazed high and wide.
Gylfi Sigurdsson was the best player on the pitch and the Icelandic midfielder forced Jakupovic into a great save just after the hour with a curling free-kick the keeper did well to tip round the post.
Alfie Mawson set up a tense finish when he pulled a goal back in injury time with a glancing header from a Sigurdsson free-kick.
1. A game Hull had to win
This was your classic six-pointer if ever there was one but it was Hull who needed the three points more than Swansea. They began the day second from bottom, four points from safety and six points behind the Swans in 16th.
The Tigers knew only a win would do if they were to stand any realistic chance of surviving. Under Marco Silva Hull have beaten Liverpool and Man Utd at home but they very rarely threatened Fabianski in the visitors’ goal until Oumar Niasse entered the fray. His two-goal blast could prove to be crucial come May.
2. Hull’s survival is now in their own hands
It’s a big, big ask, but the target for Hull is simple. History shows that five wins will be needed to give them any chance of beating the drop.
A daunting trip to an in-form Everton is up next but after that The Tigers have home games against West Ham, Middlesbrough, Watford and Sunderland.
They will have to win all of those games in the hope that when they go to Crystal Palace on the penultimate weekend and entertain Spurs on the final day, they are still in with a shout.
3. Silva reputation continues to grow
Make no mistake, for 63 minutes Hull were second best but Marco Silva may have made the best substitution of his career.
The Portuguese threw on Everton striker Niasse to partner Abel Hernandez up front, who had seen very little of the ball in way of chances. However, the pair linked up superbly for the opening goal just six minutes after Niasse’s arrival. Hernandez was involved in the second too, when his presence in the area allowed the ball to run through for Niasse to smash home.
Hull have not found goals easy to come by and with leading scorer Robert Snodgrass being sold in January, all eyes were on Niasse and Hernandez to keep Hull up. The pair showed here that they are up to the challenge.
4. Injuries prove costly for Swans
Paul Clement was forced into two substitutions before the half-time whistle. The sight of one of them, Fernando Llorente, limping off will have no doubt caused some concern for the visitors.
The Spaniard has been instrumental in Swansea’s surge out of the bottom three, having scored three goals in his last two games. Giving Clement another headache was Angel Rangel, who was forced off on 33 minutes.
Rangel was in for Kyle Naughton, who is sidelined with a hamstring injury, meaning the Swans boss could have a real headache for next week’s crucial game at Bournemouth.
5. Swans must tighten up at the back to survive
Like Hull, the Swans also have favourable home games with the likes of Middlesbrough, Stoke and West Brom still to travel to the Liberty Stadium.
They will need to tighten up at the back though. The 61 goals they have shipped so far this season is the highest in the league and they had only kept one clean sheet in their previous 12 league games when they arrived at the KCOM Stadium. They defended well in the first half and limited Hull to only a handful of half chances.
Brave keeping from Lukasz Fabianski five minutes before the break with Hernandez ready to pounce ensured the score remained goalless at half-time but a much-needed clean sheet eluded them when Hull turned the screw late on.