Any concerns over the two-game ban for star striker Jamie Vardy were brushed aside as the home side scored two goals in each half for a comfortable victory.
It left Claudio Ranieri's men eight points clear of second-placed Tottenham Hotspur, which hosts West Bromwich Albion Monday night.
With only three games remaining, Leicester, 5,000-1 outsiders at the start of the season, needs five points to clinch the title after 10 wins in the last 13 matches of a remarkable season.
Algerian star Riyad Mahrez -- who was voted PFA Player of the Year award later that evening -- opened the scoring for the Foxes with an assured finish after a mistake by Swansea's Welsh international defender Ashley Williams.
Argentina's Leonardo Ulloa, standing in for 22-goal Vardy, then showed his worth by heading home a Danny Drinkwater free kick just before the interval.
Swansea started the second half with a bit more intensity, but the game was effectively over as a contest when Ulloa tapped in from close range after good work by Jeff Schlupp.
Substitute Marc Albrighton added a fourth to round off a convincing win ahead of Leicester's tough next fixture at Manchester United next Sunday.
Ranieri praised the spirit of his team after another peerless performance.
"Fantastic performance. Without Jamie, everyone made something more. I love to see my players fighting together," he was quoted on the Leicester City Twitter feed.
The Italian, having ruled out any chance of his side winning the title until recently, if finally accepting that it is within sight.
"We had a dream. Now we must fight to make the dream a reality," he added.
Earlier Sunday, relegation battlers Sunderland held Arsenal to a goalless draw at the Stadium of Light, a result which did little for the two sides at either end of the table.
Sunderland, which had the better of the chances with Petr Cech forced into several fine saves, is though out of the relegation zone on goal difference from Norwich, with north-east rival Newcastle only a point behind.
Arsenal, boosted by the late return as a substitute for Jack Wilshere after a 10-month injury layoff, remains in fourth place in the battle for Champions League spots.
Manchester United, which reached the FA Cup final Saturday, is five points behind but with a game in hand on the Gunners.