An inspired change shortly after the hour proved to be the turning point in a turgid affair on Humberside, as Everton loanee Niasse took both chances that fell his way to earn just a second win in seven for Hull.
The Tigers, who were made to hold on slightly when Alfie Mawson pulled one back in added time, remain in the dropzone but are now within one point of safety and just three points adrift of their opponents.
The best chance of the first half fell the way of Wayne Routledge inside the opening 10 minutes, but the winger could not mark his return to the starting lineup with a goal.
After latching on to a smart Gylfi Sigurdsson through-ball, Routledge failed to get the better of Eldin Jakupovic from close range and the hosts slowly started to see more of the ball from that point on.
Possession did not equal chances, though, and the Tigers' only two efforts of a flat opening 45 minutes came from range as both Tom Huddlestone and Kamil Grosicki saw their shots kept out by Lukasz Fabianski.
The flow of the match was not helped by a number of niggling fouls, two of which saw the Swans forced into action to bring on reinforcements.
Hull made a better fist of things in the second half, firing away their first shot on target within two minutes of the restart as Huddlestone was again thwarted by Fabianski.
A second killer chance fell the way of Routledge 54 minutes in, but he blasted over from seven yards out when Jakupovic could only push a cross right into his path.
Sigurdsson, kept quiet on the whole, came close when a dipping free kick was well stopped by Jakupovic, which ultimately proved to be a big moment in the match.
Home boss Marco Silva was sparked into action, bringing on Niasse and going with two men up top - an inspired change that paid almost instant dividends.
Niasse scored his first by getting on the end of a first-time Abel Hernandez pass and tucking past Fabianski, before putting his foot through the ball from close range for the second to seemingly seal the vital win.
Mawson's header at the end of a whipped delivery into the box did give the visitors something to fight for in the second minute of four added on, yet it would prove to be too little too late.
Hull, whose impressive run of home form now stands at seven games without defeat, came closest to adding the fourth goal of the game through another sub in David Meyler, only for Fabianski to keep him out.