Leonardo Ulloa gave the home side a deserved lead in the 15th minute after good work from skipper Wes Morgan to make space for the Argentine to fire home.
Ulloa was not even in the starting XI an hour before kick-off, but an injury to David Nugent in the warm-up meant the former Brighton hitman was given his chance.
Andy King made sure of the win in the dying moments of the match after the hosts had missed several chances to make sure of the victory.
Swansea offered very little in attack, and looked toothless up front without the injured Bafetembi Gomis.
The result sees Nigel Pearson’s men move up to 18th, level on points with Hull above them, and give the Leicester faithful a real sense that the great escape could well be on.
Right from the word go, the hosts looked really up for the encounter on a glorious afternoon in the East Midlands and they got their reward for their endeavours as Ulloa rifled the Foxes into the lead.
A long ball was lumped into the box, Morgan held off his man, and on the run, Ulloa smashed the ball past Lukasz Fabianski in the Swansea goal to give the hosts the perfect start.
The intensity from the home side was incredible, and they should really have gone into the break with more to show for their efforts.
After the interval, Marc Albrighton and record signing Andrej Kramaric both had fantastic opportunities to double their side’s lead, but both blazed wide from good positions.
Kasper Schmeichel then produced a stunning save reminiscent of his famous father to deny Nelson Oliveira when through on goal and keep his side in front.
The chances continued to come for Pearson’s men, but Fabianski was in fine form too, and proving a tough nut to crack.
Referee Lee Probert then made a huge call to deny Leicester what looked like a penalty for a clash between Ashley Williams and Jamie Vardy.
However, in stoppage time, King popped up with another vital strike to make sure of the result.
Cambiasso’s free-kick proved too hot to handle for Fabianski, who could only fumble the ball into the path of the alert King, who bravely side-footed home to send the King Power into raptures, and give those jubilant fans real hope that they could be seeing top flight football next season.
Soccer Saturday verdict – Phil Thompson
“It was an electrifying start from Leicester. They took the energy from the crowd.Swansea didn’t know what had hit them. They’d come out for a nice day in the sun.
“This Leicester team just went for them and it took 20 minutes for Swansea to realise that. They are creating the chances, and they should have won this game by more.
“They had a nailed on penalty not given, which would have settled the nerves. Four games at home, two away, QPR on the last day. They have a great set of fixtures for any team down at the bottom.
“It was a great game. I was thinking that the energy levels of the Leicester team would have gone down, but they never stopped.”
Leicester: Schmeichel (7), Wasilewski (6), Huth (7), Morgan (7), Schlupp (7) , Albrighton (8), King (7), Cambiasso (7), Vardy (8), Ulloa (7), Kramaric (7).
Subs: De Laet (7), Drinkwater (6), Mahrez (8)
Swansea: Fabianski (6), Amat (6), Fernandez (6), Williams (6), Rangel (6), Cork (6), Shelvey (5), Routledge (7), Ki (5), Sigurdsson (6), Nelson Oliveira (5).
Subs: Emnes (6), Dyer (6), Montero (7)
Man of the Match: Marc Albrighton