Jamie Vardy has scored 26 goals against promoted teams since the start of 2014-15
The result boosts the Foxes hopes of a top-10 finish, with Watford, who have now lost 15 of their 19 home matches, remaining just above Norwich at the bottom of the table.
With Roy Hodgson's successor Rob Edwards paraded before kick-off, the afternoon had started brightly for the Hornets.
Joao Pedro's close-range effort deflected off Timothy Castagne to put them in front, and they had opportunities to extend their lead with Adam Masina hitting the crossbar and Brazilian forward Pedro seeing another effort well saved by Foxes goalkeeper Danny Ward.
However, a defensive mix-up between Masina and Craig Cathcart allowed Youri Tielemans to tee-up James Maddison for the equaliser, and from there the Foxes took control.
Another misjudgement, this time from goalkeeper Ben Foster, saw Vardy beat him to the ball to head in Leicester's second before Harvey Barnes guided Marc Albrighton's cross into the bottom left corner 22 seconds after the break.
While Pedro twice further seriously tested Ward, Watford's dismal day saw Vardy race on to Barnes' pass to prod the ball past Foster, before Barnes compounded their misery, sweeping a low effort past Foster into the bottom right corner late on.
This felt like an occasion for Watford to try and finish their final home match of a wretched season with a flourish.
However, they delivered a disappointing display which did anything but lay an optimistic foundation for next term's Championship campaign, their performance only underlining the scale of the job in front of Edwards as he watched on from the stands.
Pedro's early effort had provided the perfect start as they attempted to record their first victory at Vicarage Road since the 4-1 humbling of Manchester United in November.
But from the moment Leicester equalised they capitulated, with some hapless defending contributing to them becoming the first club to lose 15 home games in a Premier League season.
"We were architects of own downfall," Hodgson said.
"Bad mistakes led to the goals. When you analyse the goals we conceded, there isn't a lot good you could say. Crass individual errors and we find ourselves on the end of a very bad defeat.
"We've had the worst home record in all the leagues. You need your wins at home. The fans are entitled to be frustrated and upset with us and to make their opinions heard."
Hodgson's side have also conceded 46 league goals at home this term, the most by any top-flight team since 1960-61.
It represented an embarrassing send-off for Hodgson at Vicarage Road and for Foster, who also appears set to leave the club this summer.
While the pre-match focus was on goalkeeper Kasper Schmeichel's omission after 149 consecutive league appearances, by the end it was another of Leicester's 35-year-olds who had taken the headlines.
For the second game running Vardy scored twice, becoming the first Leicester player to do so in the Premier League and the second-oldest player ever after Youri Djorkaeff to accomplish that feat in the competition.
His first was all about anticipation, running clear of the last defender to reach Maddison's lofted ball before Foster and glancing his header into an unguarded net.
His second was another typical Vardy effort, running into the channel to collect Barnes' pass before sliding his shot past Foster.
By then Leicester's early woes of conceding a 16th top-flight goal from a corner were long forgotten.
"It was a fantastic win," said Leicester manager Brendan Rodgers.
"It's never easy at this stage of the season when people think you have nothing to play for. I'm proud of the players. They turned up and they were hungry right to the end. I thought the attacking part of our game was outstanding."
-- Courtesy of BBC Sport