The England striker opened the scoring for the struggling Foxes after just three minutes as he latched on to Islam Slimani's through-ball, which took out John Stones and Aleksandar Kolarov in the process, and rifled past Claudio Bravo.
No sooner had a hundred or so seconds passed that Leicester had doubled their lead thanks to Andy King's effort from just outside the area - Bravo got his fingers to the ball but it slipped through his grasp and into the net.
The shellshocked visitors were forced into a number of tactical changes by Pep Guardiola in the early stages but they were unable to withstand the Foxes' incisive attacks.
In the 20th minute, the hosts celebrated a third goal, with Riyad Mahrez's flick-on into the path of Vardy ultimately being taken round Bravo and bundled home.
Man City dominated possession for the remainder of the first half and completed four times more passes than their opponents, but remained unable to penetrate Leicester's defence.
The Foxes took their three-goal lead into the break and could easily have notched up more strikes, but Slimani's late unmarked header failed to hit the target when it was perhaps easier to score.
Guardiola's charges came out of the blocks with all guns blazing after the restart and tested Leicester's defence on a number of occasions but still failed to get onto the scoresheet.
With 12 minutes left in the game, Vardy sealed his first hat-trick since 2012 - when he was playing for non-league Fleetwood Town - courtesy of a dreadful backpass by Stones to Bravo which was pounced on and drilled home by the Foxes striker.
Leicester took their foot off the pedal and endured a somewhat nervy finish as Kolarov and Nolito struck back for the visitors late on, but the result was never in doubt as the Premier League champions were finally able to give their fans something to cheer about in the league.
The result sees the East Midlands outfit climb to 14th in the league table, four points above the drop zone, while Man City remain four points off top.