The Swans made several changes heading into the game, with skipper Garry Monk and Marcos Painter starting for the first time since October, while Leicester manager Nigel Pearson named an unchanged side.
The Foxes did their best to nullify early Swansea pressure but could only hold out for 10 minutes.
On-loan winger David Cotterill cut in from the left before unleashing a 30-yard right-footed drive that gave keeper Chris Weale no chance.
Paulo Sousa's side continued to press after breaking the deadlock and, midway through the half, Gorka Pintado forced Weale to a save from a difficult angle after breaking free.
The chance seemed to jolt Leicester into life and they would have equalised but for the heroics of Swansea goalkeeper Dorus de Vries.
The Dutchman prevented Matty Fryatt's 20-yard drive before producing a superb double save to deny King and Matt Oakley in quick succession.
King's shot from 15 yards was palmed away before Oakley's close-range follow-up was well saved by de Vries.
The home fans were frustrated by the missed chances at the Walkers Stadium but they soon had something to cheer about when Andy King equalised against the run of play.
Fryatt controlled a well-weighted long ball into the box, cut it across to King, who rifled the ball into the back of the net to finish a smart move from the home side on 39 minutes.
Pintado's right-wing cross moments after the restart caused havoc in the Leicester box but Joe Allen, Cedric van der Gun and Darren Pratley failed to connect when well placed.
Allen then had a shot that flew wide before Jordi Lopez forced Weale into a smart save with a 35-yard shot.
The home side were enjoying long spells of possession and were increasing the pressure on Swansea's defence, with Fryatt forcing De Vries into a close-range save.
But as the game became more scrappy and the clock ran down N'Guessan scored the winner with a bullet header into the bottom right corner in the 89th minute.