James Maddison added the second goal following a counterattack in injury time as Leicester climbed back in front of Manchester City, which briefly moved into second with a 4-1 win at Burnley on Tuesday.
It was Leicester’s seventh straight league win, tying its record for successive top-flight victories, set in 1963.
Vardy is also closing in on his record of scoring in 11 straight games, set in Leicester’s improbable title-winning season in 2015-16.
Watford, without a manager following the firing of Quique Sanchez Flores on Sunday, slipped seven points adrift of safety and still has just one win all campaign.
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