Having earlier hit the crossbar, Riyad Mahrez, playing his 100th Premier League match, doubled the advantage by capitalising on more sloppy defending to stab home in the 58th minute.
Marc Albrighton completed the victory with an excellent third goal off the woodwork after Jamie Vardy's break in the 93rd minute.
"I'm pleased with the result, the performance wasn't quite there but ultimately it is about the result and it is another clean sheet," Leicester City manager Craig Shakespeare told the BBC.
"When I took over, the most important thing was to be competitive, climb the table and never set a points target. Now mathematically we are safe.
"In football you have to try and win every game, of course it is difficult but we have to be pleased with what we have achieved."
In-form Leicester have claimed 22 points in 10 Premier League games since Shakespeare replaced Claudio Ranieri.
"It is not a bad return but all the credit has to go to the players. The remit was to take it (the manager's job) until the end of the season and we will then sit down and discuss it. I've not been told anything else so that's what we will do."
Leicester, who fell as low as 18th in February, climbed to ninth with 43 points from 35 games -- three more than Watford in 15th.
(Reporting by Tom Hayward; editing by Ed Osmond and Clare Fallon)
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