The Swans couldn't break their Premier League points record as they went down to a 2-0 defeat at the King Power Stadium.
Leicester were quick off the mark and took a deserved lead when Leonardo Ulloa fired home from inside the box.
The visitors improved after the break as Nelson Oliviera was denied by a fine save from Kasper Schmeichel, while Jefferson Montero saw a goalbound effort deflected just wide.
But the hosts sealed their third straight win late on as Andy King tapped home after Esteban Cambiasso's free-kick was spilled by Lukasz Fabianski.
The Swans made two changes to the side that drew with Everton last weekend.
Jordi Amat came in at left-back to replace the suspended Neil Taylor, while Nelson Oliviera was handed his second Premier League start in attack in place of the injured Bafe Gomis.
Leicester, meanwhile, made three changes to the team that beat West Brom as Ritchie de Laet, Matty James and David Nugent were replaced by Marcin Wasilewski, Andy King and Andrej Kramaric.
LEICESTER: Kasper Schmeichel, Marcin Wasilewski (Ritchie de Laet, ht), Robert Huth, Wes Morgan (capt), Marc Albrighton, Andy King, Esteban Cambiasso, Jeff Schlupp, Leonardo Ulloa (Riyad Mahrez, 68), Jamie Vardy, Andrej Kramaric (Danny Drinkwater, 74).
SUBS: Mark Schwarzer, Paul Konchesky, Matty James, Tom Lawrence.
SWANS: Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Jordi Amat, Jack Cork, Ki Sung-Yueng (Jefferson Montero, 58), Jonjo Shelvey, Wayne Routledge (Nathan Dyer, 70), Gylfi Sigurdsson, Nelson Oliviera (Marvin Emnes, 74).
SUBS: Gerhard Tremmel, Kyle Bartley, Leon Britton, Matt Grimes.
The Swans equalled their best-ever Premier League points total with a 1-1 draw against Everton last time out, while Garry Monk's men were also looking to go four league games unbeaten for the first time since January 2013.
But it was Leicester, buoyed by successive wins and backed by a vociferous home crowd, who started the brighter as they pinned the Swans back in their own half; while Jordi Amat was also shown an early yellow card for a foul on Andy King.
And the hosts were rewarded for their fast start by taking the lead after just 15 minutes.
A long ball into the penalty area by Wes Morgan wasn't dealt with by the Swans defence and after good hold-up play by Jeff Schlupp, striker Leonardo Ulloa was on hand to rifle a low shot past Lukasz Fabianski.
Leicester continued to press the visitors as Marc Albrighton curled a shot wide of the right-hand post, while the Swans' first sight of goal arrived on 24 minutes as Jonjo Shelvey fired over after being teed up by Angel Rangel.
Wayne Routledge then had the ball in the net for the visitors but his effort was ruled out for offside, and the winger nearly found himself in on goal again after a great ball over the top by Shelvey but Albrighton did well to deny him with a well-timed challenge.
Half-time: Leicester 1 Swans 0
The second half began much like the first as Leicester got themselves on the front foot, and the Foxes came close to doubling their lead just minutes after the restart as Marc Albrighton and Andrej Kramaric both shot just wide of goal.
But the Swans responded well as Jonjo Shelvey forced Kasper Schmeichel into his first real save; the Danish goalkeeper pushing away his curling effort from 20 yards out.
However, it was the hosts who came even closer on 55 minutes as Jamie Vardy's cross was met by Leonardo Ulloa but the striker couldn't keep his header down, while Kramaric rifled a half-volley over the bar.
That prompted the Swans to make their first change of the afternoon as Jefferson Montero replaced Ki Sung-Yueng just shy of the hour mark.
The Ecuadorian soon injected some pace into the attack as Monk's men enjoyed their best period of the game, with Nelson Oliviera being denied by Schmeichel from eight yards out and Shelvey seeing his low strike well held by the goalkeeper.
Both sides then made a change as Leicester goal scorer Leonardo Ulloa was replaced by Riyad Mahrez, while Wayne Routledge made way for Nathan Dyer for Swansea.
And Mahrez was quickly involved as he almost doubled the lead for Leicester. Swansea almost equalised at one end as Montero's shot was deflected just wide, but the hosts broke on the counter attack and Mahrez was superbly denied by Fabianski as he looked destined to score.
Marvin Emnes was then thrown on in the Swans' third and final change as Monk's men looked to find a route back into what was turning out to be an absorbing contest.
But Leicester responded well as Mahrez tricked his way into a good position 25 yards from goal before seeing a left-foot shot tipped round the post by Fabianski.
And the hosts made sure of all three points with one minute of normal time remaining as Esteban Cambiasso's free-kick was spilled by Fabianski and Andy King was on hand to tap home from close range.