With the Foxes hanging around the bottom of the table, it looked like a tough task from the outset, but Leicester quickly put pay to that idea with two goals in the first half minutes.
Vardy got one of those, and would go on to add two more before the night was out. The scoreline was pulled back a little in City's favour as Aleksandar Kolarov and Nolito scored late goals, but in truth it was a real thumping.
Vardy and King crown a perfect five minutes
Given City's fairly dismal defensive record this season, the home fans may well have been confident going into proceedings regarding their chances of scoring, but they wouldn't have expected goals so quickly.
A sumptuous touch from Riyad Mahrez set Islam Slimani free in a two-vs-two situation with Vardy, the Algerian sending his striking partner clear beyond the City defence, Vardy making no mistake in curling the ball across Claudio Bravo's outstretched leg and into the back of the net after two minutes.
Rattled, City immediately looked to hit back, but were further shocked as the Foxes doubled their lead before the five minute mark. Slimani was the provider once more, knocking the ball down to Andy King on the edge of the area, allowing the midfielder to bend a shot into the top left hand corner.
Slimani, having picked up two early assists, almost got on the scoresheet to make it three himself when Robert Huth presented him with a volley inside the area. However, the Algerian couldn't make good of his chance, blazing over from close range.
Mahrez magnificent as Vardy bags his second
That didn't matter to Leicester though, as they carried on running riot, Vardy getting his second of the night after 20 minutes. City again exposed for pressing too high up the pitch, a long ball from Christian Fuchs was controlled beautifully by Riyad Mahrez, who touched the ball through to Vardy as it dropped out of the sky, leaving the England forward with nothing to do but round Bravo and tap home.
With a soaked Pep Guardiola watching on from the sidelines wondering what to do to stop the onslaught, Leicester were determined to keep the pressure up. Enjoying a game where his devestating qualities were being shown constantly, Mahrez cut inside onto his left too easily, forcing a rare save from Bravo.
The Spaniard did eventually see his side begin to make some attempts at the Leicester goal, Kevin de Bruyne forcing a couple of saves from Ron-Robert Zieler, but little of note as the first half came to a close.
Entering two minutes of stoppage time, it could have been four for the Foxes. Leicester's lynchpin Mahrez again the conductor, he played a perfect ball for Marc Albrighton to cross from, but Slimani's header from the ball in flashed wide.
The Citizens did almost pull one back virtually immediately at the start of the second half. The ball dropped conveniently for Pablo Zabaleta in the area, and he was only denied by a superb Fuchs block. De Bruyne was quickest to react, but he couldn't get his effort on target.
As Raheem Sterling and Yaya Toure prepared themselves to enter the fray, Ilkay Gundogan was the next to go close. With the ball pinging off de Bruyne and towards Kelechi Iheanacho, the Nigerian controlled well to set his German teammate up, Gundogan dragging an effort wide.
Vardy seals it before City claw two back
City tried almost everything and couldn't quite force anything of real quality to open the Leicester City door, and another defensive error allowed Vardy to complete his hat-trick with 12 minutes remaining. Under pressure from substitute Shinji Okazaki, John Stones under-hit his backpass to Bravo, Vardy nipping in to again round the stranded 'keeper and make it four.
The away side did pull one back minutes later through Aleksandar Kolarov, but it was nothing more than a mere consolation. Presented with an opportunity to shoot from a free-kick just outside the area, the Serbian made no mistake, leaving Zieler with no chance as he curled into the top corner.
Kolarov would be involved again as the game entered stoppage time, with another consolation goal for City pulling it back to 4-2, making things look a little more respectable. Pulling out as an option on the left, the full-back played the ball across to Nolito, who finished past Zieler.