Rodgers, who started his tenure with a 2-1 defeat at Watford, was able to breathe a sigh of relief as England striker Vardy scored twice in the closing stages after setting up his team's opener.
The forward made a selfless contribution in the 21st minute when he beat the offside trap and laid the ball on to Youri Tielemans for the Belgian midfielder on loan from Monaco to net his first Premier League goal with a simple tap-in.
Substitute Floyd Ayite equalised shortly after the break when he surged into the penalty area and beat goalkeeper Kasper Schmeichel with a shot which took a deflection off two Leicester defenders.
Both keepers made good saves before Vardy restored Leicester's lead with a trademark finish in the 78th minute, drilling in a low shot past Sergio Rico from inside the penalty box.
Vardy sealed the home side's win with a scrambled close-range finish in the 86th minute, lifting Leicester into the 10th position and leaving Fulham second bottom and staring at relegation.
(Writing by Zoran Milosavljevic; Editing by Ed Osmond)
