Three excellent goals from Wilfred Ndidi, Riyad Mahrez and Marc Albrighton did the damage as Craig Shakespeare strengthened his bid to be named manager of last season's champions on a permanent basis.
As for Watford, Walter Mazzarri's side had their chances in the East Midlands but they have now lost three matches in a row and the Italian must fear for his future at Vicarage Road.
Leicester responded well but before the quarter-hour mark, the Hornets went close again as Tom Cleverley just missed the target from outside of the area.
Mahrez and Jamie Vardy had been quiet by their own high standards but they combined to create Leicester's first real opening, with Vardy seeing a deflected shot hit the post after he reacted fastest to his teammate's free kick.
Christian Kabasele was fortunate to avoid scoring an own goal when diverting a Christian Fuchs cross towards Heurelho Gomes's net, but Watford remained lively at the other end with Kasper Schmeichel having to pull off a tremendous save to deny Stefano Okaka from close range.
Cleverley forced another good intervention out of the Dane soon afterwards but with seven minutes of the first half remaining, Leicester took the lead as Ndidi drilled a shot into the top corner from inside of the box.
Just before the break, Mahrez came within inches of making it two but after mesmerising the Watford backline, his deflected effort cannoned back off the crossbar.
The goalmouth action continued after the restart with Vardy being denied by a solid block from Gomes after being played through on goal, and Okaka heading over the crossbar for Watford when well placed at the back post.
However, just before the hour mark, Leicester doubled their advantage through Mahrez, who took the ball past two Watford players before finding the back of the net from an acute angle.
The scoreline was harsh on Watford but they were fortunate to remain just the two goals behind as Leicester upped the tempo once the game had moved into the final quarter.
Gomes again came to his side's rescue to prevent Vardy from getting onto the scoresheet after latching on to Islam Slimani's pass, before the Algerian wasted a chance of his own after Albrighton and Mahrez had combined to present him with an opening.
Fuchs also cleared the bar with a set piece before Watford attempted to mount a late response with Niang and Cleverley forcing a double save out of Schmeichel, and Cleverley just missing the target from distance.
It appeared that Leicester would settle for just the two goals but in added-on time, Vardy presented Albrighton with the chance to net a third and it was one he took with a cool finish which entered the net via the post.