Jose Mourinho’s men found themselves 1-0 down to a Marc Albrighton goal at half-time, but they came out with much more pace and purpose after the break and goals from Didier Drogba, John Terry and Ramires turned the game on its head.
The result means that a Chelsea victory against Crystal Palace on Sunday will guarantee them an insurmountable 83-point haul, meaning they cannot be caught at the top.
Meanwhile, Leicester, who were good value for their first-half lead, remain outside the relegation places by one point.
Mourinho handed a surprise start in goal to Petr Cech in place of Thibaut Courtois, who was not 100 per cent fit according to the Chelsea boss.
Drogba was also brought in to add more physicality to their attack, but it was the hosts who started with the most muscle.
Esteban Cambiasso picked out Leonardo Ulloa with a fantastic first-time pass that sent the striker through on goal, but Ulloa’s first touch was poor and the ball squirmed away from danger.
Leicester continued to look more threatening in possession as Chelsea struggled to find any tempo to their game. Paul Konchesky forced a smart save low down to his right from Cech on 41 minutes and somehow Chelsea survived a goalmouth scramble that saw Cambiasso and Albrighton go close.
Albrighton had not scored a Premier League goal for three years before this clash but you would not have thought it judging by the way he stroked home Leicester’s goal just before half-time.
Jamie Vardy did the hard graft down the left wing and sent over a delicious cross along the wet turf which confused Cesar Azpilicueta, who slipped, and Albrighton was the man on the spot to fire home.
Strong words must have been said in the Chelsea dressing room at half-time and they came out a different animal in the second half; full of pace and determination.
It took them just three minutes to draw level and it came from a man who has made a career out of scoring big goals at big moments.
Drogba showed great striking instinct to find half a yard inside the area and Branislav Ivanovic found the striker with a fine cross, which he swept home confidently.
Leicester huffed and puffed but failed to deal with the revitalised Chelsea midfield, spearheaded by the brilliant and energetic Willian.
Drogba spurned chances to doublie his tally with a couple of wayward shots, but it was his skipper, Terry, that edged Chelsea in front with 11 minutes left.
Gary Cahill powered a header towards goal from a Cesc Fabregas corner and although Foxes ‘keeper Kasper Schmeichel tipped his header away, Terry was on hand to poke home from two yards.
The Chelsea fans were now in full voice, sarcastically singing “boring, boring, Chelsea” in response to the Arsenal fans’ chants after the 0-0 draw on Sunday.
There was nothing boring about Chelsea’s third goal, though, as they turned on the style.
Cesc Fabregas danced his way down the right flank and cut the ball back for Ramires, who still had a lot to do, but he found the top corner with a bullet of a strike from the edge of the area to put Chelsea on the cusp of a first title for five years.
Leicester: Schmeichel (6), Wasilewski (6), Huth (6), Morgan (7), Albrighton (7), King (6), Cambiasso (7), Drinkwater (7), Konchesky (6), Vardy (7), Ulloa (6).
Subs: De Laet (7), James (7), Mahrez (6).
Chelsea: Cech (6), Ivanovic (7), Cahill (6), Terry (7), Azpilicueta (6), Ramires (7), Matic (6); Willian (9), Fabregas (7), Hazard (6), Drogba (7).
Subs: Zouma (6), Mikel (6), Cuadrado (6)
Man of the match: Willian
Watch Chelsea v Crystal Palace live on Sky Sports 1 at 1.30pm on Sunday.