Supposed relegation fodder and considered a 5,000-1 shot for the title, the Foxes edged towards a first ever top-flight crown to the tune of the King Power Stadium's thunderous roar on Sunday.
Riyad Mahrez's opener was complemented by a Leonardo Ulloa brace and a Marc Albrighton strike as Swansea were beaten as soundly as a 4-0 scoreline suggests, moving City eight points clear of Tottenham ahead of the second-placed side's clash with West Brom on Monday.
Anything but a home victory at White Hart Lane could see the Foxes clinch the title at Manchester United next weekend, wrapping up one of the most remarkable triumphs in sporting history - never mind football.
Ranieri finally broke his silence on title talk ahead of a match that got off to a dream start, Mahrez blocking a poor Ashley Williams pass and showing wonderful composure to fire home.
Ulloa, in for suspended top scorer Jamie Vardy, put City further ahead by superbly nodding home a Danny Drinkwater free-kick, before turning in at the far post with 30 minutes remaining after fine work by Jeffrey Schlupp.
Substitute Marc Albrighton added extra gloss to the scoreline as the match came to a close with a chorus of "we shall not be moved" - an almighty din that rarely let up from the start of Leicester's penultimate home match of the season.
"History makes us who we are" read a banner held aloft by the home fans, whose early nerves were audible after Spurs' dominant win against Stoke and Leicester's rare slip-up against West Ham.
Palpable tension soon turned to unbridled joy, though, as Swansea captain Williams' attempt at a first-time pass hit Mahrez
It was a gift for the Algerian, who cut inside after his momentum had taken into the box and showed impressive composure to send a left-footed strike inside the near post.
Referee Mark Clattenburg was unmoved by any suggestions of handball in the build-up to the 10th-minute opener, which Swansea looked to cancel out as Federico Fernandez headed over a Gylfi Sigurdsson free-kick.
Schlupp, one of two Leicester changes, was proving a particular nuisance down the flank as Leicester tried to stave off a comeback, with an acrobatic Christian Fuchs attempt comfortably saved before Shinji Okazaki's strike was deflected wide.
Ranieri's men would not have to wait long to increase their lead as Wayne Routledge's foul on Wes Morgan led to a free-kick on the left flank, which Drinkwater curled in for Ulloa to superbly head home having got the better of Williams.
"Are you watching, Tottenham?" echoed around the King Power Stadium but Swansea tried to peg back the hosts, with Fernandez again heading over before ex-Tottenham midfielder Sigurdsson tested Kasper Schmeichel from distance.
Swansea boss Francesco Guidolin brought on Jefferson Montero and Alberto Paloschi in a bid to add more attacking nous, although it was not to bring with it an increased threat to the hosts' goal.
Leicester were far more ruthless and grabbed a third in the 60th minute thanks to Schlupp's pace and power, allowing him to beat Fernandez to the ball down the left
Williams denied his attempted pass to Ulloa but he reacted quickly to prod forwards, with the striker stretching to turn home at the far post.
Fuchs bent a free-kick wide and Schlupp forced Lukasz Fabianski into a low save as the home side looked to notch again, with Andre Ayew's header into the side-netting a rare second-half threat to City's clean sheet.
Fabianski produced a great stop to deny Andy King, on after Ulloa sustained a late knock, before City's three substitutes combined for the fourth.
Demarai Gray's fine work down the right ended with a cushioned King header that fell kindly for the January signing
Fabianski kept out his strike impressively but Albrighton was there to slam home.
TWEET OF THE MATCH
Gary Lineker @GaryLineker "Sat on my own watching the telly, jumping, cheering and even crying a little
It's what only football can do to us!"
PLAYER RATINGS
Leicester
Kasper Schmeichel: 7
Danny Simpson: 7
Robert Huth: 7
Wes Morgan: 7
Christian Fuchs: 7
Riyad Mahrez: 9
Danny Drinkwater: 7
N'Golo Kante: 7
Jeff Schlupp: 8
Shinji Okazaki: 7
Leonardo Ulloa: 8
Subs:
Demarai Gray: 7
Andy King: 6
Marc Albrighton: 7
Swansea:
Lukasz Fabianski: 5
Angel Rangel: 5
Ashley Williams: 4
Federico Fernandez: 5
Neil Taylor: 5
Leon Britton: 5
Jack Cork: 5
Leroy Fer: 5
Gylfi Sigurdsson: 5
Wayne Routledge: 5
Andre Ayew: 5
Subs:
Jefferson Montero: 5
Alberto Paloschi: 5
Ki Sung-Yueng: 5
STAR MAN:
Riyad Mahrez
The Algeria winger had not been at his dazzling best in recent weeks but he returned in style against Swansea
His goal, even if it was presented on a plate to him by Ashley Williams, settled the nerves around the King Power Stadium
He could be crowned PFA Player of the Year on Sunday and his scintillating performance against Swansea showed exactly why
MOMENT OF THE MATCH:
Mahrez scored just his fourth goal in his last 18 games when he was given an absolute gift by Williams, who had a stinker
The Algeria winger drilled in his 18th goal of the season when Williams' tame clearance hit him just outside the area
It settled any early nerves for the Foxes and set them on their way to another crucial win and a step closer to the title
VIEW FROM THE DUGOUT:
Before the game Leicester boss Claudio Ranieri had, finally, admitted the Foxes were going for the title and it could have added pressure to his side but it was a nerveless performance
The hosts were clinical and need just five points from their final three games to seal a title which they were 5,000-1 to win at the start of the season
Swansea looked to have packed their bags for the summer and they looked as uncertain as boss Fransesco Guidolin's future at the Liberty Stadium
MOAN OF THE MATCH:
Swansea have little to play for and have sealed survival but, apart from the first 10 minutes before Mahrez struck, they offered little resistance
Over 2,000 away fans had made the trip and they deserved more than seeing their side roll over as Leicester's title procession continued
Many teams have lost at the King Power Stadium this season but few have put up less fight.
WHO'S UP NEXT?
Manchester United v Leicester, Barclays Premier League (Sunday, May 1)
Swansea v Liverpool, Barclays Premier League (Sunday, May 1)
Source : PA
Source: PA