The Slovenian forward, top scorer of the English second tier, netted in the second-half after a devastating counter attack from the Swans punished the hosts who were wasteful infront of goal.
South Korean wide man Eom Ji-sung would be at the heart of the move, carrying the ball from one box to the other before teeing up Vipotnik to finish a powerful effort off the underside of the crossbar.
The hosts will look back at the game as a missed opportunity, having squandered several good opportunities, particularly in the first 45 minutes of the match, with Swansea goalkeeper Lawrence Vigouroux far busier of the two stoppers.
The Chile international saving superbly from Foxes striker Patson Daka, while captain Ricardo Pereira’s effort shaved the Swansea woodwork.
But the Swans grew into the game in the second period and would have that little bit more quality, and after Vipotnik’s predatory finish looked the only winner.
Defeat means Leicester drop to 23rd, above only Sheffield Wednesday, and they are four points from safety with just four league games remaining.
Victory for the Swans moves them up one place to 14th, climbing above Stoke City.
Head coach Vitor Matos had made three changes to their starting line-up from Easter Monday’s 2-2 draw against Middlesbrough, with Marko Stamenic and Gustavo Nunes recalled to the X1, whilst there was a rare start to January signing Leo Walta.
It would be Nunes who would be at the centre of the game’s first big moment, having been played into the penalty area by playmaker Melker Widell. Leicester defender Luke Thomas’ untimely challenge on the Brazilian sending him sprawling with the Swans bench baying for a penalty, but not seen in the eyes of referee Sam Allison.
The Swans would then be under the cosh with Leicester, who had drawn six out of their nine games under new manager Gary Rowett, searching for an opening.
Chances would come and go, though, first with playmaker Harry Winks picking out Pereira on the edge of the box to arrow an effort across the Swansea goal, shaving the far post in the process, before midfield partner Oliver Skipp would see his snap shot cleared off the line by Vipotnik following a set-piece.
Vigouroux would then be at his outstanding best to show great agility to palm away Daka’s flicked near-post header, from a Leicester corner, despite being blinded by the mid-winter sunshine as the Swans would be the happier of the two side’s to go in level at the break.
The visitors came out with more intent after the break, and with the dangerous Vipotnik turning provider, cutting back having found space on the right-hand side to pick out Widdel. The Swede’s effort, though lacked composure and drifted over the crossbar.
Then would come the moment of the match. A Leicester corner would go terribly wrong after being played to the edge of the penalty but straight to Eom. The South Korean would then go on a rampaging run from one end of the pitch to another before unselfishly playing in Vipotnik to smash home.
The Foxes threw the kitchen sink at the Swans to try to force an equaliser and came close with substitute Bobby De Cordova-Reid picking out former Newcastle centre half Jamaal Lascelles to head wide when well placed.
But that would be as good as it got for Rowett’s side as the Swans held firm to hold onto their clean sheet to pick up the three points.
Swansea City X1:
Lawrence Vigouroux; Sam Parker (Joel Ward 56), Ben Cabango (captain), Cameron Burgess, Josh Tymon; Marko Stamenic, Melker Widell (Ronald 76), Leo Walta (Goncalo Franco 56); Gustavo Nunes, Jisung Eom (Liam Cullen 72), Zan Vipotnik (Adam Idah 72).
[Lead image: Swansea City FC]
