Vardy, who was also on target for the seventh league game in a row, scored from the spot 10 minutes after the break after Jonny Evans had been awarded a soft penalty for a hand in the face from Adam Masina.
Watford, under the guidance of caretaker head coach Hayden Mullins for the first time, had kept their hosts at bay well to that point but struggled once Leicester took the lead. They were punished late on as Maddison strode through before firing into the bottom corner in injury time (90+5).
The visitors had only one shot on target all game while Harvey Barnes and Ayoze Perez both twice missed presentable chances, but a Leicester side below their best still did enough to earn three points which lift them back up to second place, and eight points off leaders Liverpool.
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