City had an early scare when inside the first minute Jobi McAnuff fired wide after a mistake by City keeper Marton Fulop and Danny Shittu headed a free-kick narrowly over.
But all that changed on 15 minutes when Iain Hume gave the Foxes the lead with a stunning strike.
Accepting a flick-on from DJ Campbell there seemed little danger, but Hume let fly from 25 yards with a shot that cannoned from the underside of the bar and into the net.
City continued to rattle Watford after the restart, striking the woodwork twice in a minute.
First Stephen Clemence crashed a 20-yard drive against the bar, before Campbell broke clear to side foot a shot against the base of the post.
But the Foxes weren't to be denied and went two up on 51 minutes when a half-cleared Clemence free-kick fell to Campbell, who guided home from close range.
And the home side were three goals to the good on 54 minutes when Clemence touched a free-kick to Alan Sheehan, whose deflected shot left the wrong-footed Mart Poom with no chance.
Leicester rewarded their exultant supporters with a fourth on 86 minutes when Mark De Vries turned a defender and beat the former Derby keeper with a curling shot from a tight angle.
Watford registered a consolation goal in time added on when Marlon King scored from the penalty spot after James Chambers had fouled King inside the area, but it was never going to spoil a good day for City.