Vardy made it 2-1 in the 78th minute to reach the century mark across all competitions and then netted his 101st goal eight minutes later to seal the win in new manager Brendan Rodgers' first home game in charge.
Youri Tielemans scored his first goal for the club midway through the first half before Floyd Ayite equalized for Fulham in the 50th. The win put Leicester into 10th place while Fulham is rooted in 19th and 13 points from safety after Southampton and Cardiff both won on Saturday.
Vardy set up the first goal as well. He was through on goal and had just goalkeeper Sergio Rico to beat but unselfishly squared for Tielemans to sidestep Tim Ream and tap into an empty net. Ayite came on at the break and scored with Fulham's first shot after he collected Calum Chambers' long ball on the right to breeze past Ben Chilwell into the area and his effort struck Harry Maguire to wrong-foot Kasper Schmeichel and roll in.
But Vardy had the final say as Kevin McDonald gifted the ball to James Maddison, who found the striker scampering clear and he slid the ball across past Rico. He scored his second by rolling in Harvey Barnes' low pass from 12 yards.
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